Welcome to my New Googology Series!

It's improved and longer this time!

Ascending-E Notation (E+)

Ascending-E Notation (E+) is an alternative extension of xE# (Extended Hyper-E Notation) because I thought that the Extensible-E System (ExE) was just too "dependent" on BEAF. (I mean, some saibianisms literally use it. / 22nd of june 2024 update: I realized that ##xE^ and /xE^ exist, but they're ill-defined.)

It works just like the latest formalized ExE component (#xE^ at the moment) but with new systems of fundamental sequences.

Before those stuff, let me introduce you a new term:

E[#] Structure: A delimiter that is in form E[B]a$a$a$...$a$a$a where a's can be anything, B is the base (typically a hyperion (#)) and $'s are delimiters.

And a few symbols:

◆ is the unchanged remainder of the expression.

■ is (the rest of) some delimiter.

△ is some delimiter that is not decomposable.

▲ is some delimiter that is decomposable.

Evaluate E◆n normally unless ◆ = [■]. In that case: E[■]n = ■^n, (E[■](■_2)*#)[n] = (E[■](■_2))^n, and (E[■]▲)[n] = E[■](▲[n])

(E◆#{■}▲)[n] = (E◆#{■}(▲[n]))

((E[■_3]◆#{■}(■_4))>(■_2*#))[n] = (E[(E[(E[...(E[(E[(E[■_3]◆#{■}(■_4))>(■_2)]◆#{■}(■_4))>(■_2)]◆#{■}(■_4))>(■_2)...]◆#{■}(■_4))>(■_2)]◆#{■}(■_4))>(■_2)]◆#{■}(■_4))>(■_2) with n E's

((E[■_2]◆#{■}(■_3))>▲)[n] = ((E[■_2]◆#{■}(■_3))>(▲[n]))

(E◆#{■}(■_2)*#)[n] = (E◆#{■}(■_2))>(E◆#{■}(■_2))>(E◆#{■}(■_2))>...>(E◆#{■}(■_2))>(E◆#{■}(■_2))>(E◆#{■}(■_2)) with n (E◆#{■}(■_2))'s

Here's the interesting part of this: # is decomposable, but ## isn't.

The 5 main rules (From xE^) still apply.

Examples

E3(E[#]#{#}#)3

= E3(E[#]#{#}#)[3]3

= E3(E[#]#{#}#[3])3

= E3(E[#]#{#}3)3

= E3(E[#](E[#]#{#}2))3

= E3(E[#](E[#](E[#]#{#}1)))3

= E3(E[#](E[#](E[#]#)))3

= E3(E[#](E[#](E[#]#)))[3]3

= ...

= E3(E[#](E[#](E[#]#[3])))3

= E3(E[#](E[#](E[#]3)))3

= E3(E[#](E[#]###))3

= E3(E[#](E[#]###))[3]3

= E3(E[#](E[#]###)[3])3

= ...

= E3(E[#](E[#]##)*(E[#]##)*(E[#]##))3

= ...

Calculation of the growth rate of E+

The notation is ready, so time to calculate the growth rate! (Delimiter -> FGH Ordinal)

E[#]# ≈ ω^ω

E[#]## ≈ ω^ω^2

E[#](E[#]#) ≈ ω^ω^ω

E[#]#{#}# ≈ ε0

E[E[#]#{#}#]#{#}# ≈ ε1

(E[#]#{#}#)># ≈ εω

(E[#]#{#}#)>(E[#]#{#}#) ≈ εε0

(E[#]#{#}##) ≈ ζ0

(E[#]#{#}###) ≈ η0

(E[#]#{#}(E[#]#)) ≈ φ(ω,0)

(E[#]#{#}#{#}#) ≈ φ(1,0,0)

(E[#]#{#}#{#}##) ≈ φ(1,1,0)

(E[#]#{#}#{#}#{#}#) ≈ φ(2,0,0)

(E[#]#{##}#) ≈ φ(ω,0,0)

(E[#]#{##}#{#}#) ≈ φ(1,0,0,0)

(E[#]#{##}#{#}##) ≈ φ(1,0,1,0)

(E[#]#{##}#{#}#{#}#) ≈ φ(1,1,0,0)

(E[#]#{##}#{##}#) ≈ φ(1,ω,0,0)

(E[#]#{##}#{##}#{#}#) ≈ φ(2,0,0,0)

(E[#]#{###}#) ≈ φ(ω,0,0,0)

(E[#]#{###}#{#}#) ≈ φ(1,0,0,0,0)

(E[#]#{###}#{###}#{#}#) ≈ φ(2,0,0,0,0)

(E[#]#{####}#{#}#) ≈ φ(1,0,0,0,0,0)

E[#]#{E[#]#}# ≈ ψ0(Ω^Ω^ω)

E[#]#{E[#]#}#{#}# ≈ ψ0(Ω^Ω^Ω)

E[#]#{E[#]#}#{#}## ≈ ψ0(Ω^(Ω^Ω+1))

E[#]#{E[#]#}#{#}#{#}# ≈ ψ0(Ω^(Ω^Ω+Ω))

E[#]#{E[#]#}#{##}# ≈ ψ0(Ω^(Ω^Ω+Ωω))

E[#]#{E[#]#}#{##}#{#}# ≈ ψ0(Ω^(Ω^Ω+Ω^2))

E[#]#{E[#]#}#{###}#{#}# ≈ ψ0(Ω^(Ω^Ω+Ω^3))

E[#]#{E[#]#}#{E[#]#}#{#}# ≈ ψ0(Ω^(Ω^Ω*2))

E[#]#{(E[#]#)*#}# ≈ ψ0(Ω^(Ω^Ω*ω))

E[#]#{(E[#]#)*#}#{#}# ≈ ψ0(Ω^Ω^(Ω+1))

E[#]#{(E[#]#)*##}#{#}# ≈ ψ0(Ω^Ω^(Ω+2))

E[#]#{(E[#]#)*(E[#]#)}#{#}# ≈ ψ0(Ω^Ω^Ω2)

E[#]#{E[#]##}#{#}# ≈ ψ0(Ω^Ω^Ω^2)

E[#]#{E[#]#{#}2}#{#}# ≈ ψ0(Ω^Ω^Ω^Ω)

E[#]#{E[#]#{#}3}#{#}# ≈ ψ0(Ω^Ω^Ω^Ω^Ω)

E[#]#{E[#]#{#}#}# ≈ ψ0(Ω_2)

E[#]#{E[E[#]#{#}#]#{#}#}# ≈ ψ0(Ω_2*2)

E[#]#{(E[#]#{#}#)>#}# ≈ ψ0(Ω_2*ω)

E[#]#{E[#]#{#}##}# ≈ ψ0(Ω_2^2)

E[#]#{E[#]#{#}(E[#]#)}# ≈ ψ0(Ω_2^ω)

E[#]#{E[#]#{#}#{#}#}# ≈ ψ0(Ω_2^Ω_2)

E[#]#{E[#]#{##}#}# ≈ ψ0(Ω_2^(Ω_2*ω))

E[#]#{E[#]#{E[#]#}#}# ≈ ψ0(Ω_2^Ω_2^ω)

E[#]#{E[#]#{E[#]#{#}#}#}# ≈ ψ0(Ω_3)

E[#]#{E[#]#{E[#]#{E[#]#{#}#}#}#}# ≈ ψ0(Ω_4)

Therefore, the growth rate of this is ψ0(Ω_ω), also known as the Buchholz's Ordinal.

Extended Ascending-E Notation (xE+)

xE+ introduces a new character called the slash (/). Once again, it's just a few new fundamental sequences.

/[1] --> Delete the slash, the [1] and the following entry.

/[n+1] = (E[#]#{/[n]}#)

This is also what I call the beginning of the slash era, at the end of the hyperion era (E# to the end of E+)

Examples:

E2/4

= E2/[4]2

= E2(E[#]#{/[3]}#)2

= E2(E[#]#{E[#]#{/[2]}#}#)2

= E2(E[#]#{E[#]#{E[#]#{/[1]}#}#}#)2

= E2(E[#]#{E[#]#{E[#]#}#}#)2

E3/*#2

= E3/3/*#1

= E3/3

= E3/[3]3

= E3(E[#]#{/[2]}#)3

= E3(E[#]#{E[#]#{/[1]}#}#)3

= E3(E[#]#{E[#]#}#)3

E3/*/4

= E3(/*/)[4]3

= E3/*(/[4])3

= E3/*(E[#]#{/[3]}#)3

= E3/*(E[#]#{E[#]#{/[2]}#}#)3

= E3/*(E[#]#{E[#]#{E[#]#{/[1]}#}#}#)3

= E3/*(E[#]#{E[#]#{E[#]#}#}#)3

Hyper-extended Ascending-E Notation (#xE+)

Let's keep going, but with a new term.

Entry: A set of delimiters that can be separated by +'s and can be added a number on

-- Successor entry: An entry that is a number or has a number > 0 added on it

-- Limit entry: An entry that is not a successor entry

/_(A+1)[1] = /_(A) where A is the rest of the subscript

/_(A+1)[n+1] = E[/_(A)]/_(A){/_(A+1)[n]}/_(A)

/_(A)[n] = /_(A[n]) if A is a limit entry

A*#[n] = A+A+A+...+A+A+A with n A's, if A*# is in an entry

(A_1+A_2+A_3+...+A_k)[n] = A_1+A_2+A_3+...+((A_k)[n]) if A_k is a delimiter

Examples:

E3/_(3)2

= E3/_(3)[2]3

= E3(E[/_(2)]/_(2){/_(3)[1]}/_(2))3

= E3(E[/_(2)]/_(2){/_(2)}/_(2))3

= E3(E[/_(2)]/_(2){/_(2)}/_(2))[3]3

= E3(E[/_(2)]/_(2){/_(2)}(/_(2)[3]))3

The array era

Here's another era! The slash era begins at xE+, and ends at the end of #xE+. (So yeah, it's really short.)

Arraying-E Notation (E,)

It's not too complicated though, let's just get to it.

[A] = A

#_1 = /

#_(A) = /_(A)

A_0 = A

[~<A>0<B>~~] = [~<B>~~] if A < B, where ~ is the rest of the array and concatenated multiple symbols mean variants

[~<A>0] = [~]

A_(B+1)[1] = A_(B) where, once again, B is some delimiter

A_(B+1)[n+1] = E[A_(B)]A_(B){A_(B+1)[n]}A_(B)

A_(B)[n] = A_(B[n]) if B is a limit entry

[#,A+1,~][1] = [#,A,~]

[#,A+1,~][n+1] = [#,A,~]_([#,A+1,~][n])

[#,¨,A,~][n] = [#,¨,A[n],~] if A is a limit entry, where ¨ is an empty string or a string with one or more separator-separated 0s

[#,¨,A+1,~][1] = [#,¨,A,~]

[#,¨,0,A+1,~][n+1] = [#,¨,[#,¨,0,A+1,~][n],A,~]

[#<n>k~] = [#,0,0,0,...,0,0,0,k~] with n 0's

 [#~<~~>0] = [#~]

[#<~~>k+1~][1] = [#<~~>k~]

[#<~~+1>k+1~][n+1] = [#<~~>[#<~~+1>k+1~][n]<~~+1>k~]

[#<~~>k+1~][n] = [#<~~[n]>1<~~>k~] if ~~ is a limit entry

Tip: If an array has <>s, it is not allowed to have commas. So here's a new rule:

[#~~~~<~~~>0<~~>~] = [#~~~~<~~~+~~>~] if ~~~ ≥ ~~

Ordinal Operator Notation (OON)

Ordinal Operator Notation (OON) is a notation that is in the form a{A}b where a and b are positive integers, and A is the ordinal. No need to talk too much; here are the rules:

Rule 1: a{1}b = a^b

Rule 2: a{A}1 = a

Rule 3: a{A+1}(b+1) = a{A}a{A+1}b

Rule 4: a{A}b = a{A[b]}a if A is a limit ordinal

However, this notation, like the Fast-growing, Hardy, and Slow-growing hierarchy, is ill-defined unless a specific choice of a system of fundamental sequences is explicitly fixed in the context.

But I got some systems of fundamental sequences to use.

Wainer Hierarchy (≤ε0)

ω[n] = n

(β+α)[n] = β+α[n]

(β^(α+1))[n] = β^α*(β[n])

α(β+1)[n] = αβ+(α[n])

(β^α)[n] = β^(α[n]) if α is a limit ordinal

(β*α)[n] = β*(α[n]) if α is a limit ordinal

ε0[0] = 0

ε0[n+1] = ω^(ε0[n])

Extended Wainer Hierarchy (<φ4(0))

This one is my extension on the Wainer Hierarchy.

εα[0] = 1 if α > 0

ε(α+1)[n+1] = εα^(ε(α+1))[n]

εα[n] = ε(α[n]) if α is a limit ordinal

ζ0[0] = 0

ζα[n+1] = ε(ζα[n])

ζ(α+1)[0] = ζα+1

ζα[n] = ζ(α[n]) if α is a limit ordinal

η0[0] = 0

ηα[n+1] = ζ(ηα[n])

η(α+1)[0] = ηα+1

ηα[n] = η(α[n]) if α is a limit ordinal

Veblen Hierarchy (<Γ0)

It has everything in the wainer hierarchy, plus these:

φα(0)[0] = 0

φ(β+1)(α)[n+1] = φβ(φ(β+1)(α)[n])

φβ(α+1)[0] = φβ(α)+1

φβ(α)[n] = φβ(α[n]) if α is a limit ordinal

φβ(α+1)[n] = φ(β[n])(φβ(α)+1) if β is a limit ordinal

φβ(0)[n] = φ(β[n])(0) if β is a limit ordinal

Finitary Veblen Function

It has everything in the veblen hierarchy, plus these:

Tip: φβ(α) = φ(β, α)

Another tip: εα = φ(1, α)

Another tip: ζα = φ(2, α)

Another tip: ηα = φ(3, α)

Another tip: Γα = φ(1, 0, α)

Let z be an empty string or a string with one or more zeroes separated by commas ("0, 0, 0, ..., 0, 0, 0") and s be an empty string or a string with one or more ordinals separated by commas ("a_1, a_2, a_3, ..., a_(k-2), a_(k-1), a_k") where a_1 > 0

φ(z, s, α) = φ(s, α)

φ(α) = ω^α

φ(s, 0)[0] = 0

φ(s, β+1, 0, z)[n+1] = φ(s, β, φ(s, β+1, 0, z)[n], z)

φ(s, β, z)[n] = φ(s, β[n], z) if β is a limit ordinal

φ(s, β, 0, z, α+1)[n] = φ(s, β[n], φ(s, β, 0, z, α)+1, z, 0) if β is a limit ordinal

φ(s, β+1, α+1)[n+1] = φ(s, β, φ(s, β+1, α+1)[n])

φ(s, β, α+1)[n] = φ(s, β[n], φ(s, β, α)+1) if β is a limit ordinal

φ(s, α+1)[0] =  φ(s, α)+1

Buchholz's hierarchy

This one will involve off of Buchholz's ψ function. It has everything in the wainer hierarchy, plus these:

Examples

We've gotten through so many hierarchies, so let's give examples of this notation.

Also, remember that I do not own any of these hierarchies (except the extension for the Wainer Hierarchy). I just put them here so that you can understand them.

3{φ(1, 2, ω, 0, 0)}3 = 3{φ(1, 2, ω, 0, 0)[3]}3 = 3{φ(1, 2, ω[3], 0, 0)}3 = 3{φ(1, 2, 3, 0, 0)}3

3{ε1+1}5 = 3{ε1}3{ε1+1}4 = 3{ε1}3{ε1}3{ε1+1}3 = 3{ε1}3{ε1}3{ε1}3{ε1+1}2 = 3{ε1}3{ε1}3{ε1}3{ε1}3{ε1+1}1 = 3{ε1}3{ε1}3{ε1}3{ε1}3 = 3{ε1}3{ε1}3{ε1}3{ε1}3 = 3{ε1}3{ε1}3{ε1}3{ε1[3]}3 = 3{ε1}3{ε1}3{ε1}3{ε0^ε1[2]}3 = 3{ε1}3{ε1}3{ε1}3{ε0^ε0^ε1[1]}3 = 3{ε1}3{ε1}3{ε1}3{ε0^ε0^ε0^ε1[0]}3 = 3{ε1}3{ε1}3{ε1}3{ε0^ε0^ε0^1}3 = 3{ε1}3{ε1}3{ε1}3{ε0^ε0^ε0}3

Other Notations

Higher-E Notation (E.)

This one is very irregular because the only reason this exists is that I want to make extremely big finite numbers.

This will probably be my last component of ExE (Hence the "higher"), but It'll be extremely strong.

It does not have a full definition. Therefore, it's ill-defined.

These are not even guaranteed and are just prototypes.

But here are some tips:

En[\2]m = En/_(/_(/_(.../_(/_(/))...)))n with m /'s

En[\3]m = En[\2]_([\2]_([\2]_(...[/2]_([/2]_([/2]))...)))n with m [/2]'s

En[\#]m = En[\m]n

En[\(#+1)]m = En[\#]_([\#]_([\#]_(...[\#]_([\#]_([\#]))...)))n with m [\#]'s.

En[\(#+#)]m = En[\(#+m)]n

En[\##]m = En[\(#+#+#+...+#+#+#)]n with m #'s

En[\/]m = En[\(E[#]#[\/](m-1))]n

En[\[\2]]m = En[\(/_(/_(/_(.../_(/_(/))...))))]n with m /'s

En[\\]m = En[\[\[\...[\[\[\/]]]...]]]n with m []'s

En[\\\]m = En[\\[\\[\\...[\\[\\[\\]]]...]]]n with m \\'s

En[[\_(2)2]]m = En[\\\...\\\]n with m \'s

En[[\_(2)3]]m = En[[\_(2)2][\_(2)2][\_(2)2]...[\_(2)2][\_(2)2][\_(2)2]]n with m [\_(2)2]'s

En[[\_(2)\]]m = En[[\_(2)[[\_(2)[[\_(2)...[[\_(2)[[\_(2)[[\_(2)]]]]]]...]]]]]]n with m [[\_(2)]]'s

En[[\_(2)\_(2)]]m = En[[\_(2)[\_(2)[\_(2)...[\_(2)[\_(2)[\_(2)]]]...]]]]n with m [\_(2)]'s

En[[[\_(3)2]]]m = En[[\_(2)\_(2)\_(2)...\_(2)\_(2)\_(2)]]n with m \_(2)'s

En[\_(#)]m = En[[[...[[[\_(m)2]]]...]]]n with m []'s

En[\_(#+#)]m = En[[[...[[[\_(#+m)]]]...]]]n with m+1 []'s

En[\_(\)]m = En[\_([\_([\_(...[\_([\_([\/])])]...)])])]n with m []'s

Limit of E.: En[\_(\_(\_(...\_(\_(\/))...)))]m

Looking at these, E. seems pretty definable. So, let's calculate its growth rate.

Tip: [\1] = /

En[\2]n = ψ(ψI(0))

En[\2]n#n = ψ(ψI(0))+1

En[\2]#n = ψ(ψI(0)+1)

En[\2]#^#n = ψ(ψI(0)+ω)

En[\2]/n = ψ(ψI(0)+Ω_ω)

En[\2][\2]n = ψ(ψI(0)2)

En(E[[\2]]#)n = ψ(ψI(0)ω)

En([\2]_2)n = ψ(Ω_(ψI(0)+ω))

En([\2]_3)n = ψ(Ω_(ψI(0)+ω2))

En[\3]n = ψ(ψI(1))

En[\#]n = ψ(ψI(ω))

En[\/]n = ψ(I)

En[\/]#n = ψ(I+1)

En[\/](#^#)n = ψ(I+ω)

Operator Notation (Beyond Linear Omega Level)

Let & and $ be the unchanged remainders of the operator. (Which may or may not be distinct.)

Let % be a } or a string with just 1's separated by }'s, with extra }'s at both ends.

Rule 1: If it's a {1}, a{1}b = a^b

Rule 2: If b = 1, a&1 = a

Rule 3: If the innermost number is a 1: a&{1}$b = a&$b

Rule 4: If the outermost number in the operator is a 1: a&{c}1%b = a&{c-1}(a&{c}1&(b-1))%a where all 1's in the outer % are replaced with a

Rule 5: Otherwise: a{&c}b = a{&(c-1)}a{&c}(b-1)

Examples

3{{2}1}5 = 3{{1}3{{2}1}4}3 = 3{3{{2}1}4}3 = 3{3{{1}3{{2}1}3}3}3 = 3{3{3{{2}1}3}3}3 = 3{3{3{{1}3{{2}1}2}3}3}3 = 3{3{3{3{{2}1}2}3}3}3 = 3{3{3{3{{1}3{{2}1}1}3}3}3}3 = 3{3{3{3{3{{2}1}1}3}3}3}3 = 3{3{3{3{3}3}3}3}3 = {3, 5, 1, 2}

3{{{3}1}1}2 = 3{{{2}3{{{3}1}1}1}3}3 = 3{{{2}3}3}3 = 3{{{2}3}2}3{{{2}3}3}2 = 3{{{2}3}2}3{{{2}3}2}3{{{2}3}3}1 = 3{{{2}3}2}3{{{2}3}2}3 = 3{{{2}3}2}3{{{2}3}1}3{{{2}3}2}2 = 3{{{2}3}2}3{{{2}3}1}3{{{2}3}1}3{{{2}3}2}1 = 3{{{2}3}2}3{{{2}3}1}3{{{2}3}1}3 = ... = {3, 2, 1, 1, 3}

Comparison with FGH

n{1}n = f_2(n)

n{2}n = f_3(n)

n{n}n = f_ω(n)

n{{2}1}n = f_ω+1(n)

n{{2}2}n = f_ω+2(n)

n{{2}n}n = f_ω2(n)

n{{3}n}n = f_ω3(n)

n{{n}n}n = f_ω^2(n)

n{{{2}n}n}n = f_ω^2*2(n)

n{{{n}n}n}n = f_ω^3(n)

n{{{...{{{n}n}n}...n}n}n}n with n {}'s = f_ω^ω(n)

So it has the growth rate of a linear array in BEAF.

Extended Operator Notation

a{1(1)c}b = a{{{{...{{{a}a}a}...a}a}a}a(1)c-1}a with b a's in total

C Function

I featured this in my old googology series, but it was ill-defined because I did not declare the domains of n and m. But I want to give it another try.

Rule 1: Without any slashes: aCb = a*b where a and b are positive integers

Rule 2: Last entry is 1: #/1 = # where # is the rest of the expression

Rule 3: The number before C is 1: 1C# = 1

Rule 4: First entry after C is >1: aCb/# = (a*b)C1/#

Rule 5: Otherwise, aC$/1/d/# = aC$/((a-1)C$1/d/#)/(d-1)/# where $ is a bunch of 1's separated by slashes, and the 1's in the outer one become a (also, d is a positive integer too, and has to be greater than 1)

Examples

3C1/3 = 3C(2C1/3)/2 = 3C(2C(1C1/3)/2)/2 = 3C(2C1/2)/2 = 3C(2C(1C1/2)/1)/2 = 3C(2C(1C1/2))/2 = 3C(2C1)/2 = 3C2/2 = (3*2)C1/2 = 6C1/2 = 6C(5C1/2) = ... = 6C(5C(4C(3C(2C(1C1/2))))) = 6C(5C(4C(3C(2C1)))) = 6C(5C(4C(3C2))) = ... = 720 = 6!

Fact learned: nC1/2 = n!

4C1/3 = 4C(3C1/3)/2 = ... (See above) ... = 4C720/2 = 2880C1/2 = ... (See the "fact learned" above) ... = 2880!

5C1/3 = 5C(4C1/3)/2 = ... (See above) ... = 5C(2880!)/2 = (2880!*5)C1/2 = ... (See the "fact learned" above) = (2880!*5)!

3C1/1/2 = 3C3/(2C1/1/2)/1 = 3C3/(2C2/(1C1/1/2)/1)/1 = 3C3/(2C2/(1C1/1/2)/1) = 3C3/(2C2/(1C1/1/2)) = 3C3/(2C2/(1C1/1/2)) = 3C3/(2C2/1) = 3C3/(2C2) = 3C3/4 = 9C1/4 = ...

Approximations in FGH

aCa ≈  f_1(a)

aC1/2 ≈ f_2(a)

aCa/2 ≈ f_2(f_1(a))

aC(aCa/2)/2 ≈ f_2(f_2(f_1(a)))

aC1/3 ≈ f_3(a)

aC1/4 ≈ f_4(a)

aC1/a ≈ f_ω(a)

aC1/1/2 ≈ f_ω+1(a)

aC1/2/2 ≈ f_ω+2(a)

aC1/a/2 ≈ f_ω2(a)

aC1/1/3 ≈ f_ω2+1(a)

aC1/a/a ≈ f_ω^2(a)

aC1/1/1/2 ≈ f_ω^2+1(a)

aC1/a/1/2 ≈ f_ω^2+ω(a)

aC1/a/2/2 ≈ f_ω^2+ω2(a)

aC1/a/a/2 ≈ f_ω^2*2(a)

aC1/a/a/3 ≈ f_ω^2*3(a)

aC1/a/a/a ≈ f_ω^3(a)

aC1/a/a/a/a ≈ f_ω^4(a)

aC1/a/a/a/.../a/a/a ≈ f_ω^ω(a) (The limit of linear C function)

Extended C Function

This extension uses multiple slashes between numbers. It's rules are:

Rule 1: Without any slashes: aCb = a*b

Rule 2: Last entry is 1: #1 = #

Rule 3: The number before C is 1: 1C# = 1

Rule 4: First entry after C is >1: aCb/# = (a*b)C1/#

Rule 5: If x < y: aC#1(/^x)1(/^y)#_2 = aC#1(/^y)#_2 where (/^k) is ///.../// with k /'s

Rule 6: First >1 entry comes right after multiple slashes: aC$(/^x)b# = aC$(/^(x-1))1(/^(x-1))1...1(/^(x-1))1(/^(x-1))2(/^x)b-1# with a (/^(x-1))'s

Rule 7: Otherwise, aC$/1/d/# = aC$/((a-1)C$1/d/#)/(d-1)/# where all the 1's in $ are replaced with a's

Examples

3C1//2 = 3C1/1/1/2//1 = 3C1/1/1/2 = 3C3/3/(2C1/1/1/2)/1 = 3C3/3/(2C1/1/1/2) = 3C3/3/(2C2/2/(1C1/1/1/2)/1) = 3C3/3/(2C2/2/1/1) = 3C3/3/(2C2/2) = 3C3/3/(4C1/2) = 3C3/3/4! = 3C3/3/24 = ...

3C1///2////4 = 3C1//1//1//2///1////4 = 3C1//1//1//2////4 = 3C1//1//1/1/1/2//1////4 = 3C1//1//1/1/1/2////4 = ...

Comparison with FGH

nC1//2 ≈ f_ω^ω(n)

nCn//2 ≈ f_ω^ω(f_1(n))

nC1/2//2 ≈ f_ω^ω+1(n)

nC1/n//2 ≈ f_ω^ω+ω(n)

nC1/n/n//2 ≈ f_ω^ω+ω^2(n)

nC1//3 ≈ f_ω^ω*2(n)

nC1//n ≈ f_ω^(ω+1)(n)

nC1//1/2 ≈ f_ω^(ω+1)+1(n)

nC1//n/2 ≈ f_ω^(ω+1)*2(n)

nC1//n/n ≈ f_ω^(ω+2)(n)

nC1//1//2 ≈ f_ω^ω2(n)

nC1///2 ≈ f_ω^ω^2(n)

nC1////2 ≈ f_ω^ω^3(n)

nC1/////.../////2 ≈ f_ω^ω^ω(n) (Limit of this extension)

Extensible-X System (EXS)

Similarly to ExE, this "chain" notation is made of a couple of components (1 for now)

• Hyper-X Notation

Hyper-X Notation (X#)

Here are the rules for a,b#A. Also, all lowercase variables refer to positive integers, and all UPPERCASE variables refer to an X-structure.

Base rule: With a 1 after #: a,b#1 = a^b

Prime rule: If the prime is 1: a,1#A = a

Recursion rule: If A is a successor structure: a,b#A = a,(a,(b-1)#A)#(A-1)

Catastrophic rule: Otherwise: a,b#A = a,a#(A[b])

Fundamental sequences

X[n] = n

(A+B)[n] = A+(B[n])

(A*(m+1))[n] = A*m+(A[n])

(A*B)[n] = A*(B[n]) if B is a limit structure

A^(B+1)[n] = A^B*(A[n])

(A^B)[n] = A^(B[n]) if B is a limit structure

(B,X#A)[n] = B,n#A

(B,D*X^(C+1)#A)[n] = (B,D*X^C#A)>(B,D*X^C#A)>(B,D*X^C#A)>...>(B,D*X^C#A)>(B,D*X^C#A)>(B,D*X^C#A) if A>1

A>1 = A

(A,C#D)>(B*X)[n] = (((...(((A,C#D)>B,C#D)>B,C#D)>B,C#D...)>B,C#D)>B,C#D)>B with n ",C#D"s, if D>1

((A,C#D)>B)[n] = (A,C#D)>(B[n]) if B does not end in "*X^k" and D>1

A,B#1 = A^B

(A>B)[n] = A>(B[n])

Examples

3,4#X = 3,3#4 = 3,(3,2#4)#3 = 3,(3,3#3)#3 = ... = 3^^^^3 = 3^^^tritri

3,4#(X,X#X) = 3,3#(X,X#X)[4] = 3,3#(X,4#X) = 3,3#(X,X#4) = 3,3#(X,3#4) = 3,3#(X,(X,2#4)#3) = 3,3#(X,(X,(X,1#4)#3)#3) = 3,3#(X,(X,X#3)#3) = 3,3#(X,(X,X#3)#3)[3] = 3,3#(X,(X,X#3)[3]#3) = 3,3#(X,(X,3#3)#3) = 3,3#(X,(X,(X,2#3)#2)#3) = 3,3#(X,(X,(X,(X,1#3)#2)#2)#3) = 3,3#(X,(X,(X,X#2)#2)#3) = ... = 3,3#(X,(X,(X,(X,X#1)#1)#2)#3) = 3,3#(X,(X,(X,X^X#1)#2)#3) = 3,3#(X,(X,X^X^X#2)#3) = 3,3#(X,(X,X^X^3#2)#3) = 3,3#(X,(X,X^(X^2*3)#2)#3) = 3,3#(X,(X,X^(X^2*2+X*3)#2)#3) = 3,3#(X,(X,X^(X^2*2+X*2+3)#2)#3) = 3,3#(X,(X,X^(X^2*2+X*2+2)*3#2)#3) = 3,3#(X,(X,X^(X^2*2+X*2+2)*2+X^(X^2*2+X*2+1)*3#2)#3) = ...

2,4#(X,X^2#2) = 2,2#(X,X#2)>(X,X#2)>(X,X#2)>(X,X#2) = 2,2#(X,X#2)>(X,X#2)>(X,X#2)>(X,2#2) = 2,2#(X,X#2)>(X,X#2)>(X,X#2)>(X,X#1) = 2,2#(X,X#2)>(X,X#2)>(X,X#2)>X^X = 2,2#(X,X#2)>(X,X#2)>(X,X#2)>X^2 = 2,2#(X,X#2)>(X,X#2)>((X,X#2)>X,X#2)>X = 2,2#(X,X#2)>(X,X#2)>((X,X#2)>X,X#2)>X

Growth Rate

The growth rate of this notation is f_ψ(Ω_ω) in the fast-growing hierarchy.

Simplex Hierarchy

This is a hierarchy in the form S_α(n), where n is some number, α is the ordinal and _ means subscript.

Works like this:

S_0(n) = 1

S_α+1(n+1) = S_α(n+1)+S_α+1(n) (Base case: S_α(1) = 1)

S_α(n) = S_α[n](n) if α is a limit ordinal

For the systems of fundamental sequences, see Ordinal Operator Notation.

Examples

S_3(4) = S_2(4)+S_3(3) = S_2(4)+S_2(3)+S_3(2) = S_2(4)+S_2(3)+S_2(2)+S_3(1) = S_2(4)+S_2(3)+S_2(2)+1 = S_2(4)+S_2(3)+S_1(2)+S_2(1)+1 = S_2(4)+S_2(3)+S_1(2)+1+1 = S_2(4)+S_2(3)+S_1(2)+2 = S_2(4)+S_2(3)+S_0(2)+S_1(1)+2 = S_2(4)+S_2(3)+S_0(2)+1+2 = S_2(4)+S_2(3)+S_0(2)+3 = S_2(4)+S_2(3)+1+3 = S_2(4)+S_2(3)+4

S_ω^2*2(3) = S_ω^2+ω3(3) = S_ω^2+ω2+3(3) = S_ω^2+ω2+3(3)

Conversions

S_1(n) = n = n/1

S_2(n) = (n(n+1))/2

S_3(n) = (n(n+1)(n+2))/6

S_4(n) = (n(n+1)(n+2)(n+3))/24

In short, S_b(a) = (a(a+1)(a+2)...(a+b-3)(a+b-2)(a+b-1))/b!

Extending Notations

Now let's extend some notations because... why not.

Pound-Star Notation

My extension for this notation is called "Slashing multi-nested hyper-exploding pound-star notation" (/H#*<<>> for short) and  has the following rules.

An expression consists of one or more entries separated by groups consisting of one or more items, each of which may be either a star character (*), a carat (^), an explodon array (denoted as a colon-separated list of nonnegative integers of which at least one must be positive, wrapped in curly brackets), an at sign (@), a nested group (denoted as any valid separator group -even one containing other nesting groups or supernests- wrapped in angle brackets), a supernest (denoted as either a nonnegative integer or any valid separator group in square brackets, or an empty pair of square brackets) or a slash array (denoted as an apostrophe-separated list of nonnegative integers of which at least one must be positive, with a slash on the very left, wrapped in paranthesis). The first entry must be a pound sign (#). Subsequent entries may be either a pound sign, a single positive integer, an ordered comma-separated set of one or more nonnegative integers, of which at least one must be positive, wrapped in a single set of parentheses; or a "proto-set" denoted as a single positive integer wrapped in two pairs of parentheses.

1. Start with n=1.

2. If the final separator group is anything other than a single *:

   1. If the final item in the group is a slash array:

      1. If it only has one entry, and it's a 0, replace that slash array with n pairs of square brackets.

      2. If the last entry in the slash array is a 0, remove it and multiply n by itself.

      3. If the first entry is a 0, replace the first nonzero entry with n, and decrease the entry after that by 1.

      4. Otherwise, replace the slash array with n copies of with having their first entry decreased by 1.

   2. If the final item in the group is a supernest:

      1. If it is empty, put the current value of n in it.

      2. If it contains the number 0, replace it with an at sign.

      3. If it contains any other number, decrement the number by one and wrap the supernest in n layers of nesting groups.

      4. If it contains a separator group:

         1. If the last item in the supernest is a star character, remove it and wrap the supernest in n layers of nesting groups.

         2. Otherwise, reduce it as you would a normal separator group.

   3. If the final item in the group is any nesting group, replace it with n concatenated copies of whatever subgroup it contains.

   4. If the final item in the group is an at sign, replace it with an explodon array of n terms, of which the last term is 1 and all preceding terms are 0.

   5. If the final item in the group is an explodon array:

      1. If there are two or more terms, of which the last is 0, remove the last term.

      2. Else, if the first term is 0:

         1. If that is the only term, replace that explodon array with a carat.

         2. Else, decrement the first nonzero term by one and set all earlier terms to n.

      3. Else, replace that explodon array with n identical explodon arrays that have had the first term decremented by 1.

   6. If the final character in the group is a carat, replace it with n stars.

   7. If the final character in the group is a star, replace the final entry with a series of n identical entries whose separator groups have had the final star removed.

3. Else:

   1. If the last entry is a number, multiply n by this number, then remove it from the expression.

   2. If the last entry is a pound sign, replace it with the current n.

   3. If the last entry is a proto-set ((x)), replace it with a set of n elements, each equal to x.

   4. If the last entry is a set:

      1. If the set contains only one element, replace the set with that number raised to the power of the current n.

      2. Otherwise, if the final element is 0, remove it and increment n by 1.

      3. Otherwise, decrement the final element by 1 and increment the preceding element by n.

4. Repeat rules 2-3 until the expression is reduced to a single number. This is the value of the expression.

Examples

#*3*5 (n=1)

=#*3 (n=5)

=# (n=15)

=15

#**4*5 (n=1)

=#**4 (n=5)

=#*4*4*4*4*4 (n=5)

=#*4*4*4*4 (n=20)

=#*4*4*4 (n=80)

=#*4*4 (n=320)

=#*4 (n=1280)

=# (n=5120)

=5120

#{0:0:1}2*3

=#{0:0:1}2 (n=3)

=#{3:3:0}2 (n=3)

=#{3:3}2 (n=3)

=#{2:3}{2:3}{2:3}2 (n=3)

=#{2:3}{2:3}{1:3}{1:3}{1:3}2 (n=3)

=#{2:3}{2:3}{1:3}{1:3}{0:3}{0:3}{0:3}2 (n=3)

=...

#[@]2*5

=#[@]2 (n=5)

=#[{0:0:0:0:1}]2 (n=5)

=#[{5:5:5:5}]2 (n=5)

=...

#(/0'0'1)4*6

=#(/0'0'1)4 (n=6)

=#(/0'6'0)4 (n=6)

=#(/0'6)4 (n=36)

=#(/36'5)4 (n=36)

=#(/35'5)(/35'5)(/35'5)...(/35'5)(/35'5)(/35'5)4 (n=36)

Now here's another extension called "Proto-slashing multi-nested hyper-exploding pound-star notation" (<>/H#*<<>>):

An expression consists of one or more entries separated by groups consisting of one or more items, each of which may be either a star character (*), a carat (^), an explodon array (denoted as a colon-separated list of nonnegative integers, of which at least one must be positive, wrapped in curly brackets), an at sign (@), a nested group (denoted as any valid separator group -even one containing other nesting groups or supernests- wrapped in angle brackets), a supernest (denoted as either a nonnegative integer or any valid separator group in square brackets, or an empty pair of square brackets) or a slash array (denoted as an apostrophe-separated list of nonnegative integers, optionally wrapped in any amount of parentheses; with a slash on the very left, wrapped in parenthesis / also sub-arrays can be consecutive but cannot be separated by apostrophes). The first entry must be a pound sign (#). Subsequent entries may be either a pound sign, a single positive integer, an ordered comma-separated set of one or more nonnegative integers, of which at least one must be positive, wrapped in a single set of parentheses, or a "proto-set" denoted as a single positive integer wrapped in two pairs of parentheses.

1. Start with n=1.

2. If the final separator group is anything other than a single *:

4. 1. If the final item in the group is a slash array:

      1. Go to the rightmost array that doesn't have another array in it.

      2. If it only has one entry, and it's a 0:

         1. If it's the only array in its parent, replace that array with n entries (last one has a 1, all others have 0's).

         2. If it starts with a slash, replace that slash array with n pairs of square brackets.

         3. Otherwise, replace its parent with n consecutive copies of its parent having this array deleted.

      3. If the last entry in the slash array is a 0, remove it and multiply n by itself.

      4. If the first entry is a 0, replace the first nonzero entry with n, and decrease the entry after that by 1.

      5. Otherwise, replace the slash array with n copies of it, with having their first entry decreased by 1.

   2. If the final item in the group is a supernest:

      1. If it is empty, put the current value of n in it.

      2. If it contains the number 0, replace it with an at sign.

      3. If it contains any other number, decrement the number by one and wrap the supernest in n layers of nesting groups.

      4. If it contains a separator group:

         1. If the last item in the supernest is a star character, remove it and wrap the supernest in n layers of nesting groups.

         2. Otherwise, reduce it as you would a normal separator group.

   3. If the final item in the group is any nesting group, replace it with n concatenated copies of whatever subgroup it contains.

   4. If the final item in the group is an at sign, replace it with an explodon array of n terms, of which the last term is 1 and all preceding terms are 0.

   5. If the final item in the group is an explodon array:

      1. If there are two or more terms, of which the last is 0, remove the last term.

      2. Else, if the first term is 0:

         1. If that is the only term, replace that explodon array with a carat.

         2. Else, decrement the first nonzero term by one and set all earlier terms to n.

      3. Else, replace that explodon array with n identical explodon arrays that have had the first term decremented by 1.

   6. If the final character in the group is a carat, replace it with n stars.

   7. If the final character in the group is a star, replace the final entry with a series of n identical entries whose separator groups have had the final star removed.

5. Else:

   2. 1. If the last entry is a number, multiply n by this number, then remove it from the expression.

      2. If the last entry is a pound sign, replace it with the current n.

      3. If the last entry is a proto-set ((x)), replace it with a set of n elements, each equal to x.

      4. If the last entry is a set:

         1. If the set contains only one element, replace the set with that number raised to the power of the current n.

         2. Otherwise, if the final element is 0, remove it and increment n by 1.

         3. Otherwise, decrement the final element by 1 and increment the preceding element by n.

6. Repeat the last two rules until the expression is reduced to a single number. This is the value of the expression.

Examples

#(/((5)))2*4

=#(/((5)))2 (n=4)

=#(/((4)(4)(4)(4)))2 (n=4)

=#(/((4)(4)(4)(3)(3)(3)(3)))2 (n=4)

=#(/((4)(4)(4)(3)(3)(3)(2)(2)(2)(2)))2 (n=4)

=#(/((4)(4)(4)(3)(3)(3)(2)(2)(2)(1)(1)(1)(1)))2 (n=4)

=#(/((4)(4)(4)(3)(3)(3)(2)(2)(2)(1)(1)(1)(0)(0)(0)(0)))2 (n=4)

=#(/((4)(4)(4)(3)(3)(3)(2)(2)(2)(1)(1)(1)(0)(0)(0))((4)(4)(4)(3)(3)(3)(2)(2)(2)(1)(1)(1)(0)(0)(0))((4)(4)(4)(3)(3)(3)(2)(2)(2)(1)(1)(1)(0)(0)(0)))2 (n=4)

=...

#(/(((0))))3*9

=#(/(((0))))3 (n=9)

=#(/((0'0'0'0'0'0'0'0'1)))3 (n=9)

=#(/((0'0'0'0'0'0'0'9'0)))3 (n=9)

=#(/((0'0'0'0'0'0'0'9)))3 (n=81)

=#(/((0'0'0'0'0'0'81'8)))3 (n=81)

=...

=#(/((81'80'80'80'80'80'80'8)))3 (n=81)

=...

#(/((5))(0))2*4

=#(/((5))(0))2 (n=4)

=#(/((5)))(/((5)))(/((5)))(/((5)))2 (n=4)

=#(/((5)))(/((5)))(/((5)))(/((4)(4)(4)(4)))2 (n=4)

=...

Another extension! (Nested Proto-slashing multi-nested hyper-exploding pound-star notation, <<>>/H#*<<>>):

An expression consists of one or more entries separated by groups consisting of one or more items, each of which may be either a star character (*), a carat (^), an explodon array (denoted as a colon-separated list of nonnegative integers, of which at least one must be positive, wrapped in curly brackets), an at sign (@), a nested group (denoted as any valid separator group -even one containing other nesting groups or supernests- wrapped in angle brackets), a supernest (denoted as either a nonnegative integer or any valid separator group in square brackets, or an empty pair of square brackets) or a slash array (denoted as an apostrophe-separated list of nonnegative integers, optionally wrapped in any amount of parentheses, optionally with a slash on the very left; with a slash on the very left, wrapped in parenthesis / also sub-arrays can be consecutive but cannot be separated by apostrophes). The first entry must be a pound sign (#). Subsequent entries may be either a pound sign, a single positive integer, an ordered comma-separated set of one or more nonnegative integers, of which at least one must be positive, wrapped in a single set of parentheses, or a "proto-set" denoted as a single positive integer wrapped in two pairs of parentheses.

3. Start with n=1.

4. If the final separator group is anything other than a single *:

6. 1. If the final item in the group is a slash array:

      1. Go to the rightmost array that doesn't have another array in it.

      2. If it only has one entry, and it's a 0:

         1. If it's the only array in its parent, replace that array with n entries (last one has a 1, all others have 0's).

         2. If it starts with a slash:

            1. If it's not in another slash array, replace that slash array with n pairs of square brackets.

            2. Otherwise, replace that slash array with n pairs of paranthesis.

         3. Otherwise, replace its parent with n consecutive copies of its parent having this array deleted.

      3. If the last entry in the slash array is a 0, remove it and multiply n by itself.

      4. If the first entry is a 0, replace the first nonzero entry with n, and decrease the entry after that by 1.

      5. Otherwise, replace the slash array with n copies of it, with having their first entry decreased by 1.

   2. If the final item in the group is a supernest:

      1. If it is empty, put the current value of n in it.

      2. If it contains the number 0, replace it with an at sign.

      3. If it contains any other number, decrement the number by one and wrap the supernest in n layers of nesting groups.

      4. If it contains a separator group:

         1. If the last item in the supernest is a star character, remove it and wrap the supernest in n layers of nesting groups.

         2. Otherwise, reduce it as you would a normal separator group.

   3. If the final item in the group is any nesting group, replace it with n concatenated copies of whatever subgroup it contains.

   4. If the final item in the group is an at sign, replace it with an explodon array of n terms, of which the last term is 1 and all preceding terms are 0.

   5. If the final item in the group is an explodon array:

      1. If there are two or more terms, of which the last is 0, remove the last term.

      2. Else, if the first term is 0:

         1. If that is the only term, replace that explodon array with a carat.

         2. Else, decrement the first nonzero term by one and set all earlier terms to n.

      3. Else, replace that explodon array with n identical explodon arrays that have had the first term decremented by 1.

   6. If the final character in the group is a carat, replace it with n stars.

   7. If the final character in the group is a star, replace the final entry with a series of n identical entries whose separator groups have had the final star removed.

7. Else:

   2. 1. If the last entry is a number, multiply n by this number, then remove it from the expression.

      2. If the last entry is a pound sign, replace it with the current n.

      3. If the last entry is a proto-set ((x)), replace it with a set of n elements, each equal to x.

      4. If the last entry is a set:

         1. If the set contains only one element, replace the set with that number raised to the power of the current n.

         2. Otherwise, if the final element is 0, remove it and increment n by 1.

         3. Otherwise, decrement the final element by 1 and increment the preceding element by n.

Repeat the last two rules until the expression is reduced to a single number. This is the value of the expression.

Examples

#(/(/0))2*6

=#(/(/0))2 (n=6)

=#(/((((((0)))))))2 (n=6)

=...

This one is more like a review.

#(/(/(/0)))^^2*5

=#(/(/(/0)))^^2 (n=5)

=#(/(/(/0)))^*****2 (n=5)

=#(/(/(/0)))^****2(/(/(/0)))^****2(/(/(/0)))^****2(/(/(/0)))^****2(/(/(/0)))^****2 (n=5)

=...

I made many more extensions, but they're really unnecessary, so let's just skip to Higher-exploding Ampersand-nested Separator-multiplying Nested Proto-slashing Multi-nested Hyper-exploding Pound-star notation ({}&^*x<<>>/H#*<<>>).

Yeah, it's becoming a monstrosity.

An expression consists of one or more entries separated by groups consisting of one or more items, each of which may be either a star character (*), a carat (^), an explodon array (denoted as a colon-separated list of nonnegative integers, of which at least one must be positive, or a separator group; wrapped in curly brackets), an at sign (@), a nested group (denoted as any valid separator group -even one containing other nesting groups or supernests- wrapped in angle brackets), a supernest (denoted as either a nonnegative integer or any valid separator group in square brackets, or an empty pair of square brackets), slash array (denoted as an apostrophe-separated list of nonnegative integers, optionally wrapped in any amount of parentheses, optionally with multiple slashes and/or a separator group on the very left (the separator group comes first); with a slash on the very left, wrapped in parenthesis / also sub-arrays can be consecutive but cannot be separated by apostrophes) or an ampersand (&). The first entry must be a pound sign (#). Subsequent entries may be either a pound sign, a single positive integer, an ordered comma-separated set of one or more nonnegative integers, of which at least one must be positive, wrapped in a single set of parentheses, or a "proto-set" denoted as a single positive integer wrapped in two pairs of parentheses.

1. Start with n=1.

2. If the final separator group is anything other than a single star:

   1. If the final item is an ampersand, replace it with n x's followed by a slash and a 0, all wrapped in a pair of parantheses.

   2. If the final item in the group is a slash array:

      1.  Go to the rightmost array that doesn't have another array in it.

      2. If it only has one entry, and it's a 0:

         1.  If it's the only array in its parent, replace that array with n entries (the last one has a 1; all others have 0s).

         2.  If it has a slash:

            1. If it's not in another slash array, it only has one slash, and it does not have anything before the slash; replace that slash array with n pairs of square brackets.

            2. Otherwise:

               1. If it has multiple slashes and something before, or one or more slashes without anything before, delete a slash and get n copies of the remainder nested in the 0.

               2. If there's only one slash and any amount x's, but the separator group ends in a star, delete the star and replace the slash with n slashes.

               3. If it has only one slash, one or more slashes but not a separator group, get n copies of the array nested on the leftmost x.

               4. Otherwise, reduce the separator group before the slashes normally.

            3. Otherwise, replace its parent with n consecutive copies of its parent having this array deleted.

      3. If the last entry in the slash array is a 0, remove it and multiply n by itself.

      4. If the first entry is a 0, replace the first nonzero entry with n, and decrease the entry after that by 1.

      5. Otherwise, replace the slash array with n copies of it, with having their first entry decreased by 1.

   3. If the final item in the group is a supernest:

      1. If it is empty, put the current value of n in it.

      2. If it contains a 0, replace the supernest with an at sign.

      3. If it contains any other number, decrement the number by one and wrap the supernest in n layers of nesting groups.

      4. If it contains a separator group:

         1. If the last item in the supernest is a star character, remove it and wrap the supernest in n layers of nesting groups.

         2. Otherwise, reduce it as you would a normal separator group.

      5. If the final item in the group is any nesting group, replace it with n concatenated copies of whatever subgroup it contains.

   4. If the final item in the group is an at sign, replace it with an explodon array of n terms, of which the last term is 1 and all preceding terms are 0.

   5. If the final item in the group is an explodon array:

      1. If there are two or more terms, of which the last is 0, remove the last term.

      2. If the first term is 0:

         1. If that is the only term, replace that explodon array with a carat.

         2. Otherwise, decrement the first nonzero term by one and set all earlier terms to n.

      3. If there's nothing but a separator group:

         1. If that separator group has only a star, replace the explodon array with an ampersand.

         2. If that separator group has anything but a single star but ends in a star, replace the explodon array n copies of it with the last star removed.

         3. If that separator group has anything else, reduce it normally.

      4. Else, replace that explodon array with n identical explodon arrays that have had the first term decremented by 1.

   6. If the final character in the group is a carat, replace it with n stars.

   7. If the final character in the group is a star, replace the final entry with a series of n identical entries whose separator groups have had the final star removed.

3. Otherwise:

   1. If the last entry is a number, multiply n by this number, then remove it from the expression.

   2. If the last entry is a pound sign, replace it with the current n.

   3. If the last entry is a proto-set ((x)), replace it with a set of n elements, each equal to x.

   4. If the last entry is a set:

      1. If the set contains only one element, replace the set with that number raised to the power of the current n.

      2. If the final element is 0, remove it and increment n by 1.

      3. Otherwise, decrement the final element by 1 and increment the preceding element by n.

Repeat the last two rules until the expression is reduced to a single number. This is the value of the expression.

Examples

#{{{0:1}}}2*3

=#{{{0:1}}}2 (n=3)

=#{{{3}}}2 (n=3)

=#{{{2}{2}{2}}}2 (n=3)

=#{{{2}{2}{1}{1}{1}}}2 (n=3)

=#{{{2}{2}{1}{1}{0}{0}{0}}}2 (n=3)

=#{{{2}{2}{1}{1}{0}{0}^}}2 (n=3)

=#{{{2}{2}{1}{1}{0}{0}***}}2 (n=3)

=#{{{2}{2}{1}{1}{0}{0}**}{{2}{2}{1}{1}{0}{0}**}{{2}{2}{1}{1}{0}{0}**}}2 (n=3)

=...

#{*}2*5

=#{*}2 (n=5)

=#&2 (n=5)

=#(xxxxx/0)2 (n=5)

=#(((((xxxx/0)xxxx/0)xxxx/0)xxxx/0)xxxx/0)2 (n=5)

=#(((((((((xxx/0)xxx/0)xxx/0)xxx/0)xxx/0)xxxx/0)xxxx/0)xxxx/0)xxxx/0)2 (n=5)

=...

Growth Rate

Now let's calculate the growth rate! (The ordinals shown on the right x mean f_x(n))

• #(/0)n*n ≈ ε0 (Slashing Multi-nested Hyper-exploding Pound-star Notation)

• #(/1)n*n ≈ ε0*ω

• #(/2)n*n ≈ ε0*ω^2

• #(/0'1)n*n ≈ ε0*ω^ω

• #(/0'1)n*n ≈ ε0*ω^ω

• #(/0'0'1)n*n ≈ ε0*ω^ω^2

• #(/(0))n*n ≈ ε0*ω^ω^ω (Proto-slashing Multi-nested Hyper-exploding Pound-star Notation)

• #(/(0)(0))n*n ≈ ε0*ω^(ω^ω+1)

• #(/(1))n*n ≈ ε0*ω^(ω^ω+ω)

• #(/(2))n*n ≈ ε0*ω^(ω^ω+ω^2)

• #(/(0'1))n*n ≈ ε0*ω^(ω^ω*2)

• #(/(0'1)(0))n*n ≈ ε0*ω^(ω^ω*2+1)

• #(/(0'1)(0'1))n*n ≈ ε0*ω^(ω^ω*3)

• #(/(1'1))n*n ≈ ε0*ω^ω^(ω+1)

• #(/(2'1))n*n ≈ ε0*ω^ω^(ω+2)

• #(/(0'2))n*n ≈ ε0*ω^ω^ω2

• #(/(0'0'1))n*n ≈ ε0*ω^ω^ω^2

• #(/((0)))n*n ≈ ε0*ω^ω^ω^ω

• #(/((0)(0)))n*n ≈ ε0*ω^ω^(ω^ω+1)

• #(/((1)))n*n ≈ ε0*ω^ω^(ω^ω+ω)

• #(/((0'1)))n*n ≈ ε0*ω^ω^(ω^ω*2)

• #(/((0'0'1)))n*n ≈ ε0*ω^ω^ω^(ω^2)

• #(/(((0))))n*n ≈ ε0*ω^ω^ω^ω^ω

• #(/(((0))))n*n ≈ ε0*ω^ω^ω^ω^ω

• #(/(/0))n*n ≈ ε0^2 (Nested Proto-slashing Multi-nested Hyper-exploding Pound-star Notation)

• #(/(/0)(0))n*n ≈ ε0^2*ω

• #(/(/0)(/0))n*n ≈ ε0^3

• #(/(/1))n*n ≈ ε0^ω

• #(/(/2))n*n ≈ ε0^ω^2

• #(/(/(0)))n*n ≈ ε0^ω^ω

• #(/(/(/0)))n*n ≈ ε0^ε0

• #(/(/(/(/0))))n*n ≈ ε0^ε0

• #(//0)n*n ≈ ε1 (Multiplying Nested Proto-slashing Multi-nested Hyper-exploding Pound-star Notation)

• #(///0)n*n ≈ ε2

• #(*/0)n*n ≈ εω (Separator-multiplying Nested Proto-slashing Multi-nested Hyper-exploding Pound-star Notation)

• #(**/0)n*n ≈ εω2

• #(^/0)n*n ≈ ε(ω^2)

• #(^*/0)n*n ≈ ε(ω^2+ω)

• #(^^/0)n*n ≈ ε(ω^2*2)

• #({1}/0)n*n ≈ ε(ω^3)

• #({0:1}/0)n*n ≈ ε(ω^ω)

• #({1:1}/0)n*n ≈ ε(ω^(ω+1))

• #({0:2}/0)n*n ≈ ε(ω^ω2)

• #({0:0:1}/0)n*n ≈ ε(ω^ω^2)

• #(@/0)n*n ≈ ε(ω^ω^ω)

• #((/0)/0)n*n ≈ εε0

• #(x/0)n*n ≈ ζ0 (Nested Separator-multiplying Nested Proto-slashing Multi-nested Hyper-exploding Pound-star Notation)

• #(x/1)n*n ≈ ζ0*ω

• #(x//0)n*n ≈ ε(ζ0+1)

• #(*x/0)n*n ≈ ε(ζ0+ω)

• #(xx/0)n*n ≈ ζ1

• #&n*n ≈ ζω (Ampersand-nested Separator-multiplying Nested Proto-slashing Multi-nested Hyper-exploding Pound-star Notation)

• #{*}n*n ≈ ζω (Higher-exploding Ampersand-nested Separator-multiplying Nested Proto-slashing Multi-nested Hyper-exploding Pound-star Notation)

• #{**}n*n ≈ ζω*ω

• #{***}n*n ≈ ζω*ω^2

• #{{0}}n*n ≈ ζω*ω^ω

• #{{1}}n*n ≈ ζω*ω^(ω+1)

• #{{0:1}}n*n ≈ ζω*ω^ω2

• #{@}n*n ≈ ζω*ω^ω^ω

• #{(/0)}n*n ≈ ζω*ε0

• #{(x/0)}n*n ≈ ζω^2

• #{{(x/0)}}n*n ≈ ζω^ζω

Growth Rate: ε(ζω+1)

Fixing notations

I'm just fixing some notations here, nothing too special.

Numbers in brackets notation

This one is interesting because the creator of this notation didn't define it at all. (They just gave some tips, but that's not enough to define a notation.) Their tips will probably be enough for you to understand the notation, but not for it to be well-defined. Nevermind, enough trash talking, let's get to it.

Fun but useless fact: This definition will be ported directly from my notes.

Disclaimer: If you're reading this and you're the creator of this notation, just remember that this is your notation and I'm not trying to claim it as my own. But please give it a definition, or steal mine if you want XD

But some terms first:

Dimension: A pair of paranthesis with some stuff in it.

n-dimension. A pair of paranthesis with n in it, where n is some nonnegative number.

Dimension sequence: A series of concatenated dimensions that may or may not be distinct.

And some symbols:

◆ is some dimension sequence. It is allowed to be empty as well.

◇ is some dimension.

■ is the unchanged remainder of a dimension.

□ is the unchanged remainder of a dimension but it only allows 0s and separators. (If 2 pairs of brackets are concatenated, and they're not parantheses, put 0 in between them.)

If it's attached to dimensions and not numbers, + concatenates two dimension sequences.

Multiple concatenated symbols mean variants, where each variant may or may not be distinct from other variants.

Now the rules:

Rule 1: If there's just a 0-dimension: n(0) = 10^n = 1000...000 with n 0s

Rule 2: If the first dimension is a 0-dimension:

-- 1(0)◆ = 69◆

-- (n+1)(0)◆ = (n(0)◆)◆

Rule 3: Otherwise: n◇◆ = 69◇[n]◆

Then, the most complicated part, the fundamental sequences.

Up to ω^ω^ω

◆◇[n]◇◇◆◆ = ◆◇+◇◇[n]◆◆ if ◇ ≥ ◇◇

◆◇(0)[n]◆◆ = ◆◇[n]◇◆◆

(k+1■)[1] = (k■)

(k+1■)[n+1] = (k■)(k+1■)[n]

Up to ε0

(0)[n] = n if the 0-dimension is in something

((0)◆■)[1] = (◆■) but ◆ cannot be empty

((0)◆■)[n+1] = (◆■)((0)◆■)[n] where once again, ◆ cannot be empty

(◇◆■)[n] = (◇[n]◆■) if one of the following conditions can be satisfied:

-- ◇ is a 0-dimension but ◆ is empty.

-- ◇ is not a 0-dimension.

Up to ψ0(Ω_2)

New symbols:

★ is a bunch of 0-separated separators (which may or may not be distinct).

☆ is some separator.

▲ is the unchanged remainder of a separator.

△ is the unchanged remainder of a separator but it only allows 0s and other separators.

Then the fundamental sequences:

(0<■■>■)[n] = (0<■■>[n]■)

<▲>[n]0<▲▲> = <▲>0<▲▲>[n] if <▲> ≥ <▲▲>

(□<0>[1]k+1■) = (□<0>k■) (The paranthesis may change)

(□<0>[1](0)◆■) = (□<0>◆■) if ◆ isn't empty (The paranthesis may change)

(□<0>[1]0■) = (□■) (The paranthesis may change)

(□<0>[n+1]k+1■) = (□(□<0>[n]k+1■)<0>k■) (The paranthesis may change)

(□<0>[n+1](0)◆■) = (□(□<0>[n](0)◆■)<0>◆■) if ◆ isn't empty (The paranthesis may change)

(□<0>[n+1]0■) = (□(□<0>[n]0■)■) where the rightmost 0 in the outer □ gets deleted (The paranthesis may change)

(□◇◆■)[n] = (◇[n]◆■) if one of the following conditions can be satisfied (The paranthesis may change):

-- ◇ is a 0-dimension but ◆ is empty.

-- ◇ is not a 0-dimension.

(□<△>0■)[n] = (□<△>[n]0■) (The paranthesis may change)

(□<△>k+1■)[n] = (□<△>[n]0<△>k■) (The paranthesis may change)

(□<△>(0)◆■)[n] = (□<△>[n]0<△>k■) (The paranthesis on the outside may change)

<k+1▲>[1] = <k▲>

<k+1▲>[n+1] = <k▲>0<k+1▲>[n]

<(0)◆▲>[1] = <◆▲> if ◆ isn't empty

<(0)◆▲>[n+1] = <◆▲>0<(0)◆▲>[n] if, once again, ◆ isn't empty

<◇◆▲>[n] = <◇[n]◆▲> if one of the following conditions can be satisfied:

-- ◇ is a 0-dimension but ◆ is empty.

-- ◇ is not a 0-dimension.

Up to ψ0(Ω_2*ω)

<<<...<<<0>>>...>>>[1] with k+1 <'s and >'s = <<<...<<<0>>>...>>> with k <'s and >'s

<<<...<<<0>>>...>>>[n+1] with k+1 <'s and >'s = <<<...(k <'s)...<<<0<<<...(k+1 <'s)...<<<0>>>...(k+1 <'s)...>>>[n]0>>>...(k <'s)...>>>

The superbrackets (<>s) in the fundamental sequences up to ψ0(Ω_2) can now be multiple.

Up to ψ0(Ω_ω)

This one cannot be defined because NIBN isn't defined past 69((0<0>0)<0>0), but maybe NIBNS will make it to 69(0<0[0]0>0) and I'll be able to define it. (I wonder how does the creator generalize the brackets...)

Also, I hope I won't get sued for trying to steal the creator's notation.

Simplifying notations

This one is interesting because instead of creating, fixing, extending, etc. notations, I'll simplify them.

Little note: I do not want to offend any of the notations here, but I think some are WAY TOO complicated. (Or maybe I'm just dumb XD)

Bird's array notation

This one is fine, but it becomes a nightmare when we get past pentational arrays. However, I'll still simplify it from the beginning of the dimensional arrays because... why not? I want to bring random people's tips to reality. There won't be just some tips because they're not enough. Anyway, enough gibberish, time to get to the rules.

Let # be an empty string or a string with anything.

Let & be an empty string or a string with one or more comma-separated 1s.

Let % be an empty string or a string with one or more separators separated by 1s.

Base Rule: If there are less than 3 entries: {a} = a, {a, b} = a^b

Prime Rule: If the second entry is 1: {a, 1 #} = a.

Crop-off Rule: If the last entry is 1: {# 1} = {#}

Recursion Rule: If all entries from the third one to the one before the first one with a number greater than 1 have 1s: {a, b %, &, 1, c #} = {a, a %, &, {a, b-1 %, &, 1, c #}, c-1 #} where all the 1s in the ampersand in bold (&) are replaced with a's

Prime Recursion Rule: If the third entry is bigger than 1 and follows a comma: {a, b, c #} = {a, {a, b-1, c #}, c-1 #}

Catastrophic Rule: Otherwise... (Apply the rules for {a, b #})

1. Start with the third entry of the array.

2. If it's a 1:

   1. If it's the last entry of the array, or the following separator is bigger than the preceding one and delete the entry and the preceding separator.

   2. Otherwise, go to the next entry until the current entry has a number greater than 1.

3. Otherwise, look at your left. (You're expected to be on an entry following a separator. If not, you've done something wrong.)

   1. Change the string "A n" to "A 2 A n-1" where A is a separator and n is an integer greater than 1, then go to the first A.

   2. If the current separator is a [2]: Replace it and the following entry with b comma-separated a's. If the [2] is the first separator after b, replace the first two entries as well.

   3. Otherwise, go to the first entry of the current separator.

      1. If the first entry is greater than 1, replace the separator with b copies separated by 1s and have their first entry decreased.

      2. Otherwise, apply the entire process inside this separator with the following conditions:

• Start from step 2.

• Put "Otherwise, " at the beginning of step 3.1.

• Move step 3.3 to step 3.4, step 3.2 to step 3.3, step 3.1 to step 3.2, and create a new step 3.1: "If the current entry follows a comma, change the previous entry to b and decrease the current entry by 1."

• Add a new rule (Rule 4): "If the following separator is a hyperseparator:

1. Let k be the level of the following hyperseparator. ("\" has level 1, "¬" has level 2 and "\_(n)" has level n where _() means subscript)

2. Let p be the level of the hyperseparator with the highest level, in the separator you're inside.

3. Let A be the separator that is p-k layers outside the separator you're inside.

4. Decrease the current entry by 1.

5. Replace the previous entry with b copies of A with a 1 at the left and 2 at the right (Replace the innermost point with a 1, or a 2 if 1 can be deleted).

"

4. Change b to a.

5. End the process.

Tip: Each hyperseparator is a shorthand for the one 1 level higher wrapped inside "[1" and "2]". i.e. \ is a shorthand for [1 ¬ 2], ¬ is a shorthand for [1 \_(3) 2], \_(3) is a shorthand for [1 \_(4) 2], etc.

Also, 1 \ 1 \ 1 \ ... \ 1 \ 1 \ 2 is not to be confused with [1 ¬ 2]. Instead, it's [2 ¬ 2].

Similarly, 1 ¬ 1 ¬ 1 ¬ ... ¬ 1 ¬ 1 ¬ 2 is not to be confused with [1 \_(3) 2] (It's [2 \_(3) 2]), 1 \_(3) 1 \_(3) 1 \_(3) ... \_(3) 1 \_(3) 1 \_(3) 2 is not to be confused with [1 \_(4) 2] (It's [2 \_(4) 2]), 1 \_(4) 1 \_(4) 1 \_(4) ... \_(4) 1 \_(4) 1 \_(4) 2 is not to be confused with [1 \_(5) 2] (It's [2 \_(5) 2]), etc.

Finally, this version of bird's array notation has the growth rate of f_ψ(Ω_ω) in the fast-growing hierarchy.

Numbers I Coined

Here's a giant list of numbers I coined.

BEAF (Bowers' Exploding Array Function)

• Little Googondol = {10, 100, 10}

• Little Googoadol = {10, 100, 11}

• Little Goograndol = {10, 100, 12}

• Little Googreadol = {10, 100, 13}

• Little Googigandol = {10, 100, 14}

• Little Googorgedol = {10, 100, 15}

• Little Googuldol = {10, 100, 16}

• Little Googaspdol = {10, 100, 17}

• Little Googinordol = {10, 100, 18}

• Little Googarganduul = {10, 100, 19}

• Little Googonkosol = {10, 100, 20}

• Little Googoakosol = {10, 100, 21}

• Little Googrankosol = {10, 100, 22}

• Little Googreakosol = {10, 100, 23}

• Little Googigankosol = {10, 100, 24}

• Little Googorgekosol = {10, 100, 25}

• Little Googulkosol = {10, 100, 26}

• Little Googaspkosol = {10, 100, 27}

• Little Googinorkosol = {10, 100, 28}

• Little Googargankosuul = {10, 100, 29}

• Little Googontritol = {10, 100, 30}

• Little Googoatritol = {10, 100, 31}

• Little Goograntritol = {10, 100, 32}

• Little Googreatritol = {10, 100, 33}

• Little Googigantritol = {10, 100, 34}

• Little Googorgetritol = {10, 100, 35}

• Little Googultritol = {10, 100, 36}

• Little Googasptritol = {10, 100, 37}

• Little Googinortritol = {10, 100, 38}

• Little Googargantrituul = {10, 100, 39}

• Little Googonsartol = {10, 100, 40}

• Little Googoasartol = {10, 100, 41}

• Little Googransartol = {10, 100, 42}

• Little Googreasartol = {10, 100, 43}

• Little Googigansartol = {10, 100, 44}

• Little Googorgesartol = {10, 100, 45}

• Little Googulsartol = {10, 100, 46}

• Little Googaspsartol = {10, 100, 47}

• Little Googinorsartol = {10, 100, 48}

• Little Googargansartuul = {10, 100, 49}

• Little Googonpetol = {10, 100, 50}

• Little Googoapetol = {10, 100, 51}

• Little Googranpetol = {10, 100, 52}

• Little Googreapetol = {10, 100, 53}

• Little Googiganpetol = {10, 100, 54}

• Little Googorgepetol = {10, 100, 55}

• Little Googulpetol = {10, 100, 56}

• Little Googasppetol = {10, 100, 57}

• Little Googinorpetol = {10, 100, 58}

• Little Googarganpetuul = {10, 100, 59}

• Little Googonextol = {10, 100, 60}

• Little Googoaextol = {10, 100, 61}

• Little Googranextol = {10, 100, 62}

• Little Googreaextol = {10, 100, 63}

• Little Googiganextol = {10, 100, 64}

• Little Googorge-extol = {10, 100, 65}

• Little Googulextol = {10, 100, 66}

• Little Googaspextol = {10, 100, 67}

• Little Googinorextol = {10, 100, 68}

• Little Googarganextuul = {10, 100, 69}

• Little Googoneptol = {10, 100, 70}

• Little Googoaeptol = {10, 100, 71}

• Little Goograneptol = {10, 100, 72}

• Little Googreaeptol = {10, 100, 73}

• Little Googiganeptol = {10, 100, 74}

• Little Googorge-eptol = {10, 100, 75}

• Little Googuleptol = {10, 100, 76}

• Little Googaspeptol = {10, 100, 77}

• Little Googinoreptol = {10, 100, 78}

• Little Googarganeptuul = {10, 100, 79}

• Little Googonogdol = {10, 100, 80}

• Little Googoaogdol = {10, 100, 81}

• Little Googranogdol = {10, 100, 82}

• Little Googreaogdol = {10, 100, 83}

• Little Googiganogdol = {10, 100, 84}

• Little Googorgeogdol = {10, 100, 85}

• Little Googulogdol = {10, 100, 86}

• Little Googaspogdol = {10, 100, 87}

• Little Googinorogdol = {10, 100, 88}

• Little Googarganogduul = {10, 100, 89}

• Little Googonentol = {10, 100, 90}

• Little Googoaentol = {10, 100, 91}

• Little Googranentol = {10, 100, 92}

• Little Googreaentol = {10, 100, 93}

• Little Googiganentol = {10, 100, 94}

• Little Googorge-entol = {10, 100, 95}

• Little Googulentol = {10, 100, 96}

• Little Googaspentol = {10, 100, 97}

• Little Googinorentol = {10, 100, 98}

• Little Googarganentuul = {10, 100, 99}

• Little Gugold (Alternatively Little Googonhectol) = {10, 100, 100}

• Gopplexathoth = 10^^10^^100 & 10

• Kunplexulus = 10^^^10^^^100 & 10

• Quadrunplexulus = 10^^^^10^^^^100 & 10

• Quintunplexulus = 10^^^^^10^^^^^100 & 10

• Gootrawamba (Normally Goobawantra) = {10, 100 (1) 3} & 10

• Gooquadrawamba (Normally Goobawanquadra) = {10, 100 (1) 4} & 10

• Goppatrix (Normally Quathragoth) = 10^^100 & 10 & 10

• Lineatetrix = 10 & 10 & 10 & 10 = {10, 10 (1) 2} & 10 & 10

• Goobawantra (Normally Elemongulus) = 100 & 10 & 10 & 10 = {10, 100 (1) 2} & 10 & 10

• Lineapentix = 10 & 10 & 10 & 10 & 10 = {10, 10 (1) 2} & 10 & 10 & 10

• Lineahexix = 10 & 10 & 10 & 10 & 10 & 10 = {10, 10 (1) 2} & 10 & 10 & 10 & 10

• Lineaheptix = {10, 7 / 2}

• Linea-octix = {10, 8 / 2}

• Linea-ennix = {10, 9 / 2}

• Lineadektix (Normally Dekulus) = {10, 10 / 2}

• Linea-icosix = {10, 20 / 2}

• Linea-triantix = {10, 30 / 2}

• Linea-sarantix = {10, 40 / 2}

• Linea-penintix = {10, 50 / 2}

• Linea-exintix = {10, 60 / 2}

• Linea-ebdomintix = {10, 70 / 2}

• Linea-ogdontix = {10, 80 / 2}

• Linea-enenintix = {10, 90 / 2}

• Gooblol (Alternatively Linea-hectix, normally The Whopper) = {10, 100 / 2} (Fun fact: I referred to this number as legiattic goobol in my old googology series. The only reason I call this number differently is that I wanted it to have a more generalized name.)

• Gibblol = {10, 100, 2 / 2}

• Gabblol = {10, 100, 3 / 2}

• Geeblol = {10, 100, 4 / 2}

• Giblol = {10, 100, 5 / 2}

• Gobblol = {10, 100, 6 / 2}

• Gablol = {10, 100, 7 / 2}

• Booblol = {10, 10, 100 / 2}

• Corpolral = {10, 100, 1, 2 / 2}

• Mulpolral = {10, 100, 2, 2 / 2}

• Powpolral = {10, 100, 3, 2 / 2}

• Bibblol = {10, 10, 100, 2 / 2}

• Babblol = {10, 10, 100, 3 / 2}

• Beeblol = {10, 10, 100, 4 / 2}

• Biblol = {10, 10, 100, 5 / 2}

• Bobblol = {10, 10, 100, 6 / 2}

• Bablol = {10, 10, 100, 7 / 2}

• Trooblol = {10, 10, 10, 100 / 2}

• Goobol-blol = {10, 100 (1) 2 / 2}

• Gootrol-blol = {10, 100 (1) 3 / 2}

• Gossol-blol = {10, 10 (1) 100 / 2}

• Mossol-blol = {10, 10 (1) 10, 100 / 2}

• Dubol-blol = {10, 100 (1)(1) 2 / 2}

• Dossol-blol = {10, 10 (1)(1) 100 / 2}

• Goxxol-blol = {10, 100 (2) 2 / 2}

• Coloxxol-blol = {10, 100 (3) 2 / 2}

• Teroxxol-blol = {10, 100 (4) 2 / 2}

• Petoxxol-blol = {10, 100 (5) 2 / 2}

• Ectoxxol-blol = {10, 100 (6) 2 / 2}

• Zettoxxol-blol = {10, 100 (7) 2 / 2}

• Yottoxxol-blol = {10, 100 (8) 2 / 2}

• Xenoxxol-blol = {10, 100 (9) 2 / 2}

• Dekaloxxol-blol = {10, 100 (10) 2 / 2}

• Icosaloxxol-blol = {10, 100 (20) 2 / 2}

• Triantaloxxol-blol = {10, 100 (30) 2 / 2}

• Sarantaloxxol-blol = {10, 100 (40) 2 / 2}

• Penintaloxxol-blol = {10, 100 (50) 2 / 2}

• Exintaloxxol-blol = {10, 100 (60) 2 / 2}

• Ebdomintaloxxol-blol = {10, 100 (70) 2 / 2}

• Ogdontaloxxol-blol = {10, 100 (80) 2 / 2}

• Enenintaloxxol-blol = {10, 100 (90) 2 / 2}

• Gongulus-blol = {10, 100 (0, 1) 2 / 2}

• Bongulus-blol = {10, 100 (0, 0, 1) 2 / 2}

• Goplexulus-blol = {10, 100 ((1) 1) 2 / 2}

• Goppatoth-blol = {10^^100 & 10 / 2}

• Kungulus-blol = {10^^^100 & 10 / 2}

• Quadrunculus-blol = {10^^^^100 & 10 / 2}

• Humongulus-blol = {10{100}10 & 10 / 2}

• Goobawamba-blol = {100 & 10 & 10 / 2}

• Goobawantra-blol (Alternatively Elemongulus-blol) = {100 & 10 & 10 & 10 / 2}

• Gootlol = {10, 100 / 3}

• Gooquadlol = {10, 100 / 4}

• Goslol = {10, 10 / 100}

• Moslol = {10, 10 / 10, 100}

• Goobllol (Formerly dublol) = {10, 100 // 2}

• Gooblllol (Formerly trublol) = {10, 100 /// 2}

• Goobolegion = {10, 100 (1)/ 2}

• Goxxolegion = {10, 100 (2)/ 2}

• Gongulegion = {10, 100 (0, 1)/ 2}

• Goplexulegion = {10, 100 ((1)1)/ 2}

• Goppalegion = {L, X^^X}_(10,100)

• Kungulegion = {L, X^^^X}_(10,100)

• Quadrunculegion = {L, X^^^^X}_(10,100)

• Humongulegion = {L, X{X}X}_(10,100)

• Linealegitrix = 10 @ 10 @ 10

• Goobalegiamba = 100 @ 10  @ 10

• Linealegitetrix = 10 @ 10 @ 10 @ 10

• Goobalegiantra = 100 @ 10 @ 10 @ 10

• Goobaol = {L2, 1}_10,100

• Goobuol = {L3, 1}_10,100

• Little meameamealokkapoowa = {LX, 1}_10,100

• Goobloldupe = {LL, 1}_10,100

• Goobloltrupe = {LLL, 1}_10,100

• Gooblolongulus = {X & L, 1}_10,100

• Goobloloplexulus = {X^100 & L, 1}_10,10

• Gooblothoth = {10^^100 & L, 1}_10,10

• Gooblologuludupe = {L & L, 1}_10,10

• Gooblologooblol = {{L, L / 2}, 1}_10,100

• Gooblologooblologooblol = {{{L, L / 2}, 1}_(L, L), 1}_10,100

• Gooblologooblologooblologooblol = {{{{L, L / 2}, 1}_(L, L), 1}_(L, L), 1}_10,100

• Gooblasphemorgulus = {{{{{...{{{{{L, L / 2}, 1}_(L, L), 1}_(L, L), 1}_(L, L), 1}_(L, L), 1...}_(L, L), 1}_(L, L), 1}_(L, L), 1}_(L, L), 1}_(10, 100) where there are 100 arrays in total

Extensible-E System

• Googolnovemnonagintiplex (Normally Grangol) = E100#100

• Grand Grangol (Alternatively Googolnovemnonagintiplexidex, normally Grangoldex) = E100#100#2

• Grand Grand Grangol (Alternatively Googolnovemnonagintiplexidudex, normally Grangoldudex) = E100#100#3

• Googolnovemnonagintiplexinovemnonagintidex (Normally Greagol) = E100#100#100

• Googolnovemnonagintiplexinovemnonagintidexinovemnonagintithrexinovemnonagintitetrexinovemnonagintipentexinovemnonagintihexinovemnonagintiheptexinovemnonaginti-octexinovemnonaginti-ennex (Normally Googondol) = E100#100#100#100#100#100#100#100#100#100

• Googolnovemnonagintiplexinovemnonagintidexinovemnonagintithrexinovemnonagintitetrexinovemnonagintipentexinovemnonagintihexinovemnonagintiheptexinovemnonaginti-octexinovemnonaginti-ennexinovemnonagintidecexinovemnonaginti-undecexinovemnonagintiduodecexinovemnonagintitredecexinovemnonagintiquattordecexinovemnonagintiquindecexinovemnonagintisexdecexinovemnonagintiseptemdecexinovemnonaginti-octadecexinovemnonaginti-novemdecexinovemnonagintivigintexinovemnonaginti-unvigintexinovemnonagintiduovigintexinovemnonagintitrevigintexinovemnonagintiquattorvigintexinovemnonagintiquinvigintexinovemnonagintisexvigintexinovemnonagintiseptemvigintexinovemnonaginti-octavigintexinovemnonaginti-novemvigintexinovemnonagintitrigintexinovemnonaginti-untrigintexinovemnonagintiduotrigintexinovemnonagintitretrigintexinovemnonagintiquattortrigintexinovemnonagintiquintrigintexinovemnonagintisextrigintexinovemnonagintiseptemtrigintexinovemnonaginti-octatrigintexinovemnonaginti-novemtrigintexinovemnonagintiquadragintexinovemnonaginti-unquadragintexinovemnonagintiduoquadragintexinovemnonagintitrequadragintexinovemnonagintiquattorquadragintexinovemnonagintiquinquadragintexinovemnonagintisexquadragintexinovemnonagintiseptemquadragintexinovemnonaginti-octaquadragintexinovemnonaginti-novemquadragintexi...novemnonagintinovemnonagintinovemnonagintinovemnonagintex (Normally Gugold) = E100##100

• Googolcentex = E100#1#1#1#...#1#1#1#2 where there are 100 #'s

• Googolmillex = E100#1#1#1#...#1#1#1#2 where there are 1,000 #'s

• Googolmicrex = E100#1#1#1#...#1#1#1#2 where there are 1,000,000 #'s

• Googolnanex = E100#1#1#1#...#1#1#1#2 where there are 1,000,000,000 #'s

• Godgahlah-plexed-grangol (Formerly godgahlah-plexed-googol) = E100#^#1#2

• Godgahlah-plexed-gugold = E100#^#2#2

• Godgahlah-plexed-throogol = E100#^#3#2

• Godgahlah-plexed-pentoogol = E100#^#5#2

• Godgahlah-plexed-dektoogol = E100#^#10#2

• Godgahlah-plexed-icosolus = E100#^#20#2

• Godgahlah-plexed-godgahlah (Normally Grand Godgahlah) = E100#^#100#2

• Godgahlah-dexed-googol = E100#^#1#1#2

• Godgahlah-suplexed = E100#^#100##1#2

• Gotrigahlah-plexed-godgahlah = E100#^#100#^#1#2

• Godgahlah-by-hyperion (Normally Godgoldgahlah) = E100#^#*#100 (Fun fact: I featured this in my old googology series)

• Godgahlah-by-deutero-hyperion (Normally Godthroogahlah) = E100#^#*##100

• Godgahlah-by-trito-hyperion (Normally Godtetroogahlah) = E100#^#*###100

• Godgahlah-by-teterto-hyperion = E100#^#*####100

• Godgahlah-by-pepto-hyperion = E100#^#*#####100

• Godgahlah-by-exto-hyperion = E100#^#*######100 = E100#^#*#^#6

• Godgahlah-by-epto-hyperion = E100#^#*#^#7

• Godgahlah-by-ogdo-hyperion = E100#^#*#^#8

• Godgahlah-by-ento-hyperion = E100#^#*#^#9

• Godgahlah-by-dekato-hyperion = E100#^#*#^#10

• Godgahlah-by-isosto-hyperion = E100#^#*#^#20

• Godgahlah-by-trianto-hyperion = E100#^#*#^#30

• Godgahlah-by-saranto-hyperion = E100#^#*#^#40

• Godgahlah-by-peninto-hyperion = E100#^#*#^#50

• Godgahlah-by-exinto-hyperion = E100#^#*#^#60

• Godgahlah-by-ebdominto-hyperion = E100#^#*#^#70

• Godgahlah-by-ogdonto-hyperion = E100#^#*#^#80

• Godgahlah-by-eneninto-hyperion = E100#^#*#^#90

• Godgahlah-by-godgahlah (Alternatively Godgahlah-by-hecato-hyperion, Normally Deutero-godgahlah) =  E100#^#*#^#100

Extended Cascading-E Notation (xE^)

• Godhecatathol (Alternatively ascended grangol, normally Tethrathothitoth) = E100#^^#101

• Tethrigridi-iterator (Normally Tethritergriditerator) = E100#^^#>(##+#)100

• Tethrigridi-diterator (Normally Tethriditergriditerator) = E100#^^#>(##+#+#)100

• Tethrigridi-triterator (Normally Tethritritergriditerator) = E100#^^#>(##+#+#)100

• Tethridigriditerator (Normally Throotrigol-turreted-tethrathoth) = E100#^^#>(##+##)100

• Tethritrigriditerator (Normally Throotergol-turreted-tethrathoth) = E100#^^#>(##+##+##)100

• Tethricubicul-iterator = E100#^^#>(###+#)100

• Tethridecicul-nonicul-octicul-septicul-sexticul-quinticul-quarticul-cubicul-gridi-iterator = E100#^^#>(#^10+#^9+#^8+#^7+#^6+#^5+####+###+##+#)100

• Tethrato-deutero-gralgathor = E100#^^(#^#^##*#^#^##)100

• Tethrato-gralgathorfact = E100#^^#^(#^##*#)100

• Tethrato-gralgathordeus = E100#^^#^(#^##*#^##)100

• Tethrarxihendeck = E100#^^^#11

• Tethrarxidodeck = E100#^^^#12

• Tethrarxitriadeck = E100#^^^#13

• Tethrarxitetradeck = E100#^^^#14

• Tethrarxipentadeck = E100#^^^#15

• Tethrarxihexadeck = E100#^^^#16

• Tethrarxiheptadeck = E100#^^^#17

• Tethrarxi-octadeck = E100#^^^#18

• Tethrarxi-ennadeck = E100#^^^#19

• Tethrarxihenicose = E100#^^^#21

• Tethrarxidoicose = E100#^^^#22

• Tethrarxitricose = E100#^^^#23

• Tethrarxitetricose = E100#^^^#24

• Tethrarxipenticose = E100#^^^#25

• Pentoocthulhum (Normally Tethrarxi-googliad) = E100#^^^#(E100)

• Pentacthulhum-plexed-tethrathoth = E100#^^^#2#2

• Pentacthulhum-plexed-tethrato-tethrathoth (Alternatively Pentacthulhum-plexed-tethrarxitri) = E100#^^^#3#2

• Pentacthulhum-plexed-pentacthulhum (Normally Grand Pentacthulhum) = E100#^^^#100#2

• Pentacthulhum-duplexed-googol = E100#^^^#1#3

• Pentacthulhum-triplexed-googol = E100#^^^#1#4

• Pentacthulhum-dexed-googol = E100#^^^#1#1#2

• Pentacthulhum-dexed-tethrathoth = E100#^^^#2#1#2

• Pentacthulhum-suplexed = E100#^^^#100##1#2

• Pentacthulhum-dusuplexed = E100#^^^#100##1#3

• Pentacthulhum-sudexed = E100#^^^#100##1#1#2

• Pentacthulhum-plexitris = E100#^^^#100##100##1#2

• Pentadeucthulhum (Normally Pentacthuldugon) = E100(#^^^#)^^^#100

• Pentacthulspatialator (Normally Godgahlah-turreted-pentacthulhum) = E100#^^^#>#^#100

• Pentacthulsuperspatialator (Alternatively Godgathor-turreted-pentacthulhum) = E100#^^^#>#^#^#100

• Hexacthulditerator = E100#^^^#>(#+#)100

• Hexacthultriterator = E100#^^^#>(#+#+#)100

• Hexacthulgriditerator = E100#^^^#>##100

• Hexacthulgridi-iterator = E100#^^^#>(##+#)100

• Hexacthulgridi-diterator = E100#^^^#>(##+#+#)100

• Hexacthuldigriditerator = E100#^^^#>(##+##)100

• Hexacthuldigridi-iterator = E100#^^^#>(##+##+#)100

• Hexacthultrigriditerator = E100#^^^#>(##+##+##)100

• Hexacthulcubiculator = E100#^^^#>###100

Hyper-Extended Cascading-E Notation (#xE^)

• Astraliagog = E100#{#}#149,597,870,700 (149,597,870,700 is the amount of meters in an astronomical unit)

Godsgodgahlah regiment

• Godsgodgahlah = E100#{#+1}#100

• Godsgodarxichill (Formerly godsgodgularxichill) = E100#{#+1}#1,000

• Godsgodarximyr (Formerly godsgodgularximyr) = E100#{#+1}#10,000

• Godsgodarximegas (Formerly godsgodgularximega) = E100#{#+1}#1,000,000

• Godsgoogahlah = E100#{#+1}#(E100)

• Grand godsgodgahlah = E100#{#+1}#100#2

• Grand grand godsgodgahlah = E100#{#+1}#100#3

• Three-ex-grand godsgodgahlah = E100#{#+1}#100#4

• Four-ex-grand godsgodgahlah = E100#{#+1}#100#5

• Five-ex-grand godsgodgahlah = E100#{#+1}#100#6

• Six-ex-grand godsgodgahlah = E100#{#+1}#100#7

• Seven-ex-grand godsgodgahlah = E100#{#+1}#100#8

• Eight-ex-grand godsgodgahlah = E100#{#+1}#100#9

• Nine-ex-grand godsgodgahlah = E100#{#+1}#100#10

• Ten-ex-grand godsgodgahlah = E100#{#+1}#100#11

• Eleven-ex-grand godsgodgahlah = E100#{#+1}#100#12

• Twelve-ex-grand godsgodgahlah = E100#{#+1}#100#13

• Thirteen-ex-grand godsgodgahlah = E100#{#+1}#100#14

• Fourteen-ex-grand godsgodgahlah = E100#{#+1}#100#15

• Fifteen-ex-grand godsgodgahlah = E100#{#+1}#100#16

• Sixteen-ex-grand godsgodgahlah = E100#{#+1}#100#17

• Seventeen-ex-grand godsgodgahlah = E100#{#+1}#100#18

• Eighteen-ex-grand godsgodgahlah = E100#{#+1}#100#19

• Nineteen-ex-grand godsgodgahlah = E100#{#+1}#100#20

• Twenty-ex-grand godsgodgahlah = E100#{#+1}#100#21

• Thirty-ex-grand godsgodgahlah = E100#{#+1}#100#31

• Forty-ex-grand godsgodgahlah = E100#{#+1}#100#41

• Fifty-ex-grand godsgodgahlah = E100#{#+1}#100#51

• Sixty-ex-grand godsgodgahlah = E100#{#+1}#100#61

• Seventy-ex-grand godsgodgahlah = E100#{#+1}#100#71

• Eighty-ex-grand godsgodgahlah = E100#{#+1}#100#81

• Ninety-ex-grand godsgodgahlah = E100#{#+1}#100#91

• Grangol-carta-godsgodgahlah = E100#{#+1}#100#100

• Hundred-ex-grand godsgodgahlah = E100#{#+1}#100#101

• Thousand-ex-grand godsgodgahlah = E100#{#+1}#100#1,001

• Million-ex-grand godsgodgahlah = E100#{#+1}#100#1,000,001

• Googol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100)

• Grangol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#100)

• Greagol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#100#100)

• Gigangol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#100#100#100)

• Gorgegol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#100#100#100#100)

• Gulgol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100##6)

• Gaspgol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100##7)

• Ginorgol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100##8)

• Gargantuul-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100##9)

• Googondol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100##10)

• Gugold-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100##100)

• Gugolthra-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100##100##100)

• Gugoltesla-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100###4)

• Gugolpeta-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100###5)

• Gugoldeka-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100###10)

• Throogol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100###100)

• Tetroogol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100####100)

• Pentoogol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#####100)

• Godgahlah-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^#100)

• Gridgahlah-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^##100)

• Kubikahlah-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^###100)

• Godgathor-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^#^#100)

• Godtothol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^#^#^#100)

• Godtertol-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^#^#^#^#100)

• Tethrathoth-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^^#100)

• Tethriterator-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^^#>#100)

• Tethracross-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^^##100)

• Tethracubor-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^^###100)

• Tethratope-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^^#^#100)

• Tethrato-tethrathoth-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^^#^^#100)

• Pentacthulhum-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^^^#100)

• Pentacthulcross-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^^^##100)

• Pentacthultope-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^^^#^#100)

• Hexacthulhum-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#^^^^#100)

• Godsgodgulus-ex-grand godsgodgahlah = E100#{#+1}#100#(1+E100#{#}#100)

• Grand grangol-carta-godsgodgahlah = E100#{#+1}#100#100#2

• Grand grand grangol-carta-godsgodgahlah = E100#{#+1}#100#100#3

• Three-ex-grand grangol-carta-godsgodgahlah = E100#{#+1}#100#100#4

• Four-ex-grand grangol-carta-godsgodgahlah = E100#{#+1}#100#100#5

• Five-ex-grand grangol-carta-godsgodgahlah = E100#{#+1}#100#100#6

• Six-ex-grand grangol-carta-godsgodgahlah = E100#{#+1}#100#100#7

• Seven-ex-grand grangol-carta-godsgodgahlah = E100#{#+1}#100#100#8

• Eight-ex-grand grangol-carta-godsgodgahlah = E100#{#+1}#100#100#9

• Nine-ex-grand grangol-carta-godsgodgahlah = E100#{#+1}#100#100#10

• Ten-ex-grand grangol-carta-godsgodgahlah = E100#{#+1}#100#100#11

• Greagol-carta-godsgodgahlah = E100#{#+1}#100#100#100

• Gigangol-carta-godsgodgahlah = E100#{#+1}#100#100#100#100

• Gorgegol-carta-godsgodgahlah = E100#{#+1}#100#100#100#100#100

• Gulgol-carta-godsgodgahlah = E100#{#+1}#100##6

• Gaspgol-carta-godsgodgahlah = E100#{#+1}#100##7

• Ginorgol-carta-godsgodgahlah = E100#{#+1}#100##8

• Gargantuul-carta-godsgodgahlah = E100#{#+1}#100##9

• Googondol-carta-godsgodgahlah = E100#{#+1}#100##10

• Gugold-carta-godsgodgahlah = E100#{#+1}#100##100

• Gugolthra-carta-godsgodgahlah = E100#{#+1}#100##100##100

• Throogol-carta-godsgodgahlah = E100#{#+1}#100###100

• Tetroogol-carta-godsgodgahlah = E100#{#+1}#100####100

• Godgahlah-carta-godsgodgahlah = E100#{#+1}#100#^#100

• Gridgahlah-carta-godsgodgahlah = E100#{#+1}#100#^##100

• Godgathor-carta-godsgodgahlah = E100#{#+1}#100#^#^#100

• Godtothol-carta-godsgodgahlah = E100#{#+1}#100#^#^#^#100

• Tethrathoth-carta-godsgodgahlah = E100#{#+1}#100#^^#100

• Tethracross-carta-godsgodgahlah = E100#{#+1}#100#^^##100

• Tethratope-carta-godsgodgahlah = E100#{#+1}#100#^^#^#100

• Pentacthulhum-carta-godsgodgahlah = E100#{#+1}#100#^^^#100

• Hexacthulhum-carta-godsgodgahlah = E100#{#+1}#100#^^^^#100

• Godsgodgulus-carta-godsgodgahlah = E100#{#+1}#100#{#}#100

• Godsgodgularxitri-carta-godsgodgahlah = E100#{#+1}#100#{#}#{#}#100

• Godsgodgularxitet-carta-godsgodgahlah = E100#{#+1}#100#{#}#{#}#{#}#100

• Godsgodgularxipent-carta-godsgodgahlah = E100#{#+1}#100#{#}#{#}#{#}#{#}#100

• Godsgodgularxideck-carta-godsgodgahlah = E100#{#+1}#100#{#+1}#10

• Godsgodgahlah-by-deuteron = E100#{#+1}#100#{#+1}#100

• Godsgodgahlah-by-triton = E100#{#+1}#100#{#+1}#100#{#+1}#100

• Godsgodgahlah-by-teterton = E100#{#+1}#*#5

• Godsgodgahlah-by-pepton = E100#{#+1}#*#6

• Godsgodgahlah-by-exton = E100#{#+1}#*#7

• Godsgodgahlah-by-epton = E100#{#+1}#*#8

• Godsgodgahlah-by-ogdon = E100#{#+1}#*#9

• Godsgodgahlah-by-enton = E100#{#+1}#*#10

• Godsgodgahlah-by-dekaton = E100#{#+1}#*#11

• Godsgodgahlah-by-hyperion = E100#{#+1}#*#100

• Godsgodgahlah-by-deutero-hyperion = E100#{#+1}#*##100

• Godsgodgahlah-by-trito-hyperion = E100#{#+1}#*###100

• Godsgodgahlah-by-teterto-hyperion = E100#{#+1}#*####100

• Godsgodgahlah-by-pepto-hyperion = E100#{#+1}#*#####100

• Godsgodgahlah-by-dekato-hyperion = E100#{#+1}#*#^#10

• Godsgodgahlah-by-godgahlah = E100#{#+1}#*#^#100

• Godsgodgahlah-by-gridgahlah = E100#{#+1}#*#^##100

• Godsgodgahlah-by-kubikahlah = E100#{#+1}#*#^###100

• Godsgodgahlah-by-quarticahlah = E100#{#+1}#*#^####100

• Godsgodgahlah-by-quinticahlah = E100#{#+1}#*#^#####100

• Godsgodgahlah-by-decicahlah = E100#{#+1}#*#^#^#10

• Godsgodgahlah-by-godgathor = E100#{#+1}#*#^#^#100

• Godsgodgahlah-by-godtothol = E100#{#+1}#*#^#^#^#100

• Godsgodgahlah-by-godtertol = E100#{#+1}#*#^#^#^#^#100

• Godsgodgahlah-by-tethrathoth = E100#{#+1}#*#^^#100

• Godsgodgahlah-by-tethriterator = E100#{#+1}#*#^^#>#100

• Godsgodgahlah-by-tethracross = E100#{#+1}#*#^^##100

• Godsgodgahlah-by-tethratope = E100#{#+1}#*#^^#^#100

• Godsgodgahlah-by-pentacthulhum = E100#{#+1}#*#^^^#100

• Godsgodgahlah-by-godsgodgulus = E100#{#+1}#*#{#}#100

• Deutero-godsgodgahlah = E100#{#+1}#*#{#+1}#100

• Trito-godsgodgahlah = E100#{#+1}#*#{#+1}#*#{#+1}#100

• Teterto-godsgodgahlah = E100(#{#+1}#)^#4

• Pepto-godsgodgahlah = E100(#{#+1}#)^#5

• Exto-godsgodgahlah = E100(#{#+1}#)^#6

• Epto-godsgodgahlah = E100(#{#+1}#)^#7

• Ogdo-godsgodgahlah = E100(#{#+1}#)^#8

• Ento-godsgodgahlah = E100(#{#+1}#)^#9

• Dekato-godsgodgahlah = E100(#{#+1}#)^#10

• Godsgodgahlahfact = E100(#{#+1}#)^#100

• Godsgodgahlahgridifact = E100(#{#+1}#)^##100

• Godsgodgahlah-ipso-godgahlah = E100(#{#+1}#)^#^#100

• Godsgodgahlah-ipso-godgathor = E100(#{#+1}#)^#^#^#100

• Godsgodgahlah-ipso-tethrathoth = E100(#{#+1}#)^#^^#100

• Godsgodgahlah-ipso-tethriterator = E100(#{#+1}#)^(#^^#>#)100

• Godsgodgahlah-ipso-tethracross = E100(#{#+1}#)^#^^##100

• Godsgodgahlah-ipso-tethratope = E100(#{#+1}#)^#^^#^#100

• Godsgodgahlah-ipso-pentacthulhum = E100(#{#+1}#)^#^^^#100

• Godsgodgahlah-ipso-godsgodgulus = E100(#{#+1}#)^(#{#}#)100

• Dutetrated-godsgodgahlah = E100(#{#+1}#)^(#{#+1}#)100

• Tritetrated-godsgodgahlah = E100(#{#+1}#)^(#{#+1}#)^(#{#+1}#)100

• Terrible godsgodgahlah = E100(#{#+1}#)^^#100

• Two-ex-terrible godsgodgahlah = E100((#{#+1}#)^^#)^^#100

• Territerated godsgodgahlah = E100(#{#+1}#)^^#>#100

• Terrisquared godsgodgahlah = E100(#{#+1}#)^^##100

• Terricubed godsgodgahlah = E100(#{#+1}#)^^###100

• Territoped godsgodgahlah = E100(#{#+1}#)^^#^#100

• Horrible godsgodgahlah = E100(#{#+1}#)^^^#100

• Horritoped godsgodgahlah = E100(#{#+1}#)^^^#^#100

• Horrendous godsgodgahlah = E100(#{#+1}#)^^^^#100

• Godsgorrendous godsgodgahlah = E100(#{#+1}#){#}#100

• Duplicated-godsgodgahlah = E100(#{#+1}#){#+1}#100

• Triplicated-godsgodgahlah = E100((#{#+1}#){#+1}#){#+1}#100,

• Godsgodgahiterator = E100#{#+1}#>#100

• Godsgodgahditerator = E100#{#+1}#>(#+#)100

• Godsgodgahtriterator = E100#{#+1}#>(#+#+#)100

• Godsgodgahgriditerator = E100#{#+1}#>##100

• Godsgodgahgridi-iterator = E100#{#+1}#>(##+#)100

• Godsgodgahgridi-diterator = E100#{#+1}#>(##+#+#)100

• Godsgodgahgridi-triterator = E100#{#+1}#>(##+#+#+#)100

• Godsgodgahdigriditerator = E100#{#+1}#>(##+##)100

• Godsgodgahdigridi-iterator = E100#{#+1}#>(##+##+#)100

• Godsgodgahdigridi-diterator = E100#{#+1}#>(##+##+#+#)100

• Godsgodgahdigridi-triterator = E100#{#+1}#>(##+##+#+#+#)100

• Godsgodgahtrigriditerator = E100#{#+1}#>(##+##+##)100

• Godsgodgahcubiculator = E100#{#+1}#>###100

• Godsgodgahcubicul-iterator = E100#{#+1}#>(###+#)100

• Godsgodgahcubicul-diterator = E100#{#+1}#>(###+#+#)100

• Godsgodgahcubicul-triterator = E100#{#+1}#>(###+#+#+#)100

• Godsgodgahcubicul-griditerator = E100#{#+1}#>(###+##)100

• Godsgodgahcubicul-gridi-iterator = E100#{#+1}#>(###+##+#)100

• Godsgodgahcubicul-gridi-diterator = E100#{#+1}#>(###+##+#+#)100

• Godsgodgahcubicul-digriditerator = E100#{#+1}#>(###+##+##)100

• Godsgodgahcubicul-digridi-iterator = E100#{#+1}#>(###+##+##+#)100

• Godsgodgahcubicul-trigriditerator = E100#{#+1}#>(###+##+##+##)100

• Godsgodgahducubiculator = E100#{#+1}#>(###+###)100

• Godsgodgahducubicul-iterator = E100#{#+1}#>(###+###+#)100

• Godsgodgahducubicul-diterator = E100#{#+1}#>(###+###+##)100

• Godsgodgahtricubiculator = E100#{#+1}#>(###+###+###)100

• Godsgodgahquarticulator = E100#{#+1}#>####100

• Godsgodgahduquarticulator = E100#{#+1}#>(####+####)100

• Godsgodgahquinticulator = E100#{#+1}#>#####100

• Godsgodgahsexticulator = E100#{#+1}#>(#^6)100

• Godsgodgahsepticulator = E100#{#+1}#>(#^7)100

• Godsgodgahocticulator = E100#{#+1}#>(#^8)100

• Godsgodgahnoniculator = E100#{#+1}#>(#^9)100

• Godsgodgahdeciculator = E100#{#+1}#>(#^10)100

• Godsgodgahdecicul-nonicul-octicul-septicul-sexticul-quinticul-quarticul-cubicul-gridi-iterator = E100#{#+1}#>(#^10+#^9+#^8+#^7+#^6+#^5+####+###+##+#)100

• Godsgodgahspatialator (Alternatively godgahlah-turreted-godsgodgahlah) = E100#{#+1}#>#^#100

• Godgoldgahlah-turreted-godsgodgahlah = E100#{#+1}#>(#^#*#)100

• Godthroogahlah-turreted-godsgodgahlah = E100#{#+1}#>(#^#*##)100

• Deutero-godgahlah-turreted-godsgodgahlah = E100#{#+1}#>(#^#*#^#)100

• Trito-godgahlah-turreted-godsgodgahlah = E100#{#+1}#>(#^#*#^#*#^#)100

• Gridgahlah-turreted-godsgodgahlah = E100#{#+1}#>#^##100

• Kubikahlah-turreted-godsgodgahlah = E100#{#+1}#>#^###100

• Godgathor-turreted-godsgodgahlah = E100#{#+1}#>#^#^#100

• Tethrathoth-turreted-godsgodgahlah = E100#{#+1}#>#^^#100

• Tethriterator-turreted-godsgodgahlah = E100#{#+1}#>#^^#>#100

• Tethracross-turreted-godsgodgahlah = E100#{#+1}#>#^^##100

• Tethratope-turreted-godsgodgahlah = E100#{#+1}#>#^^#^#100

• Pentacthulhum-turreted-godsgodgahlah = E100#{#+1}#>#^^^#100

• Hexacthulhum-turreted-godsgodgahlah = E100#{#+1}#>#^^^^#100

• Godsgodgulus-turreted-godsgodgahlah = E100#{#+1}#>#{#}#100

• Dustaculated-godsgodgahlah = E100#{#+1}#>#{#+1}#100

• Tristaculated-godsgodgahlah = E100#{#+1}#>#{#+1}#>#{#+1}#100

• Tetrastaculated-godsgodgahlah = E100#{#+1}##4

• Pentastaculated-godsgodgahlah = E100#{#+1}##5

• Dekastaculated-godsgodgahlah = E100#{#+1}##10

• Godsgodgahcross = E100#{#+1}##100

• Godsgodgahitercross = E100#{#+1}##>#100

• Dustaculated-godsgodgahcross = E100#{#+1}##>#{#+1}##100

• Godsgodgahcubor = E100#{#+1}###100

• Godsgodgahtope = E100#{#+1}#^#100

• Godsgodgahulto-godgathor = E100#{#+1}#^#^#100

• Godsgodgahulto-tethrathoth = E100#{#+1}#^^#100

• Godsgodgahulto-pentacthulhum = E100#{#+1}#^^^#100

• Godsgodgahulto-godsgodgulus = E100#{#+1}#{#}#100

• Godsgodgahulto-godsgodgahlah (Alternatively Godsgodgahularxitri) = E100#{#+1}#{#+1}#100

• Godsgodgahularxideck = E100#{#+2}#10

End of the godsgodgahlah regiment

Beginning of the godsgotethrathoth regiment

• Godsgotethrathoth = E100#{#+2}#100

• Grand godsgotethrathoth = E100#{#+2}#100#2

• Grangol-carta-godsgotethrathoth = E100#{#+2}#100#100

• Greagol-carta-godsgotethrathoth = E100#{#+2}#100#100#100

• Gugold-carta-godsgotethrathoth = E100#{#+2}#100##100

• Throogol-carta-godsgotethrathoth = E100#{#+2}#100###100

• Godgahlah-carta-godsgotethrathoth = E100#{#+2}#100#^#100

• Godgathor-carta-godsgotethrathoth = E100#{#+2}#100#^#^#100

• Tethrathoth-carta-godsgotethrathoth = E100#{#+2}#100#^^#100

• Pentacthulhum-carta-godsgotethrathoth = E100#{#+2}#100#^^^#100

• Godsgodgulus-carta-godsgotethrathoth = E100#{#+2}#100#{#}#100

• Godsgodgahlah-carta-godsgotethrathoth = E100#{#+2}#100#{#+1}#100

• Godsgotethrathoth-by-deuteron = E100#{#+2}#100#{#+2}#100

• Godsgotethrathoth-by-triton = E100#{#+2}#100#{#+2}#100#{#+2}#100

• Godsgotethrathoth-by-teterton = E100#{#+2}#*#5

• Godsgotethrathoth-by-pepton = E100#{#+2}#*#6

• Godsgotethrathoth-by-dekaton = E100#{#+2}#*#11

• Godsgotethrathoth-by-hyperion = E100#{#+2}#*#100

• Godsgotethrathoth-by-deutero-hyperion = E100#{#+2}#*##100

• Godsgotethrathoth-by-godgahlah = E100#{#+2}#*#^#100

• Godsgotethrathoth-by-tethrathoth = E100#{#+2}#*#^^#100

• Godsgotethrathoth-by-pentacthulhum = E100#{#+2}#*#^^^#100

• Godsgotethrathoth-by-godsgodgulus = E100#{#+2}#*#{#}#100

• Godsgotethrathoth-by-godsgodgahlah = E100#{#+2}#*#{#+1}#100

• Deutero-godsgotethrathoth = E100#{#+2}#*#{#+2}#100

• Trito-godsgotethrathoth = E100#{#+2}#*#{#+2}#*#{#+2}#100

• Godsgotethrafact = E100(#{#+2}#)^#100

• Godsgotethragridifact = E100(#{#+2}#)^##100

• Godsgotethrathoth-ipso-godgahlah = E100(#{#+2}#)^#^#100

• Godsgotethrathoth-ipso-godgathor = E100(#{#+2}#)^#^#^#100

• Godsgotethrathoth-ipso-tethrathoth = E100(#{#+2}#)^#^^#100

• Godsgotethrathoth-ipso-pentacthulhum = E100(#{#+2}#)^#^^^#100

• Godsgotethrathoth-ipso-godsgodgulus = E100(#{#+2}#)^#{#}#100

• Godsgotethrathoth-ipso-godsgodgahlah = E100(#{#+2}#)^#{#+1}#100

• Dutetrated-godsgotethrathoth = E100(#{#+2}#)^#{#+2}#100

• Tritetrated-godsgotethrathoth = E100(#{#+2}#)^(#{#+2}#)^#{#+2}#100

• Terrible godsgotethrathoth = E100(#{#+2}#)^^#100

• Terrisquared godsgotethrathoth = E100(#{#+2}#)^^##100

• Territoped godsgotethrathoth = E100(#{#+2}#)^^#^#100

• Horrible godsgotethrathoth = E100(#{#+2}#)^^^#100

• Horrendous godsgotethrathoth = E100(#{#+2}#)^^^^#100

• Godsgorrendous godsgotethrathoth = E100(#{#+2}#){#}#100

• Godsgodgahlah-rendous godsgotethrathoth = E100(#{#+2}#){#+1}#100

• Duplicated-godsgotethrathoth = E100(#{#+2}#){#+2}#100

• Triplicated-godsgotethrathoth = E100((#{#+2}#){#+2}#){#+2}#100

• Godsgotethriterator = E100#{#+2}#>#100

• Godsgotethriditerator = E100#{#+2}#>(#+#)100

• Godsgotethritriterator = E100#{#+2}#>(#+#+#)100

• Godsgotethrigriditerator = E100#{#+2}#>##100

• Godsgotethrigridi-iterator = E100#{#+2}#>(##+#)100

• Godsgotethrigridi-diterator = E100#{#+2}#>(##+#+#)100

• Godsgotethridigriditerator = E100#{#+2}#>(##+##)100

• Godsgotethricubiculator = E100#{#+2}#>###100

• Godsgotethriquarticulator = E100#{#+2}#>####100

• Godsgotethrispatialator = E100#{#+2}#>#^#100

• Godsgotethrisuperspatialator = E100#{#+2}#>#^#^#100

• Tethrathoth-turreted-godsgotethrathoth = E100#{#+2}#>#^^#100

• Tethracross-turreted-godsgotethrathoth = E100#{#+2}#>#^^##100

• Tethratope-turreted-godsgotethrathoth = E100#{#+2}#>#^^#^#100

• Pentacthulhum-turreted-godsgotethrathoth = E100#{#+2}#>#^^^#100

• Hexacthulhum-turreted-godsgotethrathoth = E100#{#+2}#>#^^^^#100

• Godsgodgulus-turreted-godsgotethrathoth = E100#{#+2}#>#{#}#100

• Godsgodgahlah-turreted-godsgotethrathoth = E100#{#+2}#>#{#+1}#100

• Dustaculated-godsgotethrathoth = E100#{#+2}#>#{#+2}#100

• Tristaculated-godsgotethrathoth = E100#{#+2}#>#{#+2}#>#{#+2}#100

• Godsgotethracross = E100#{#+2}##100

• Godsgotethracubor = E100#{#+2}###100

• Godsgotethrateron = E100#{#+2}####100

• Godsgotethratope = E100#{#+2}#^#100

• Godsgotethrato-godgathor = E100#{#+2}#^#^#100

• Godsgotethrato-tethrathoth = E100#{#+2}#^^#100

• Godsgotethrato-tethracross = E100#{#+2}#^^##100

• Godsgotethrato-tethratope = E100#{#+2}#^^#^#100

• Godsgotethrato-pentacthulhum = E100#{#+2}#^^^#100

• Godsgotethrato-hexacthulhum = E100#{#+2}#^^^^#100

• Godsgotethrato-godsgodgulus = E100#{#+2}#{#}#100

• Godsgotethrato-godsgodgahlah = E100#{#+2}#{#+1}#100

• Godsgotethrarxitri = E100#{#+2}#{#+2}#100

• Godsgotethrarxipent = E100#{#+2}#{#+2}#{#+2}#{#+2}#100

• Godsgotethrarxideck = E100#{#+3}#10

End of the godsgotethrathoth regiment

Beginning of the godsgopentacthulhum regiment

• Godsgopentacthulhum (Alternatively Godsgotethrarxihect) = E100#{#+3}#100

• Godsgopentacthulhuchime = E100#{#+3}#1,000

• Godsgopentacthulhutoll = E100#{#+3}#10,000

• Godsgopentacthulhugong = E100#{#+3}#100,000

• Grand godsgopentacthulhum = E100#{#+3}#100#2

End of the godsgopentacthulhum regiment

• Godsgohexacthulhum = E100#{#+4}#100

• Godsgoheptacthulhum = E100#{#+5}#100

• Godsgodekacthulhum = E100#{#+8}#100

• Godsgododekacthulhum (Alternatively godsgoliath) = E100#{#+10}#100

• Godsgodopenantacthulhum (Alternatively godsgolligog) = E100#{#+50}#100

• Godsgodeuiterator = E100#{#+#}#>#100

• Godsgodeugriditerator = E100#{#+#}#>##100

• Dustaculated-godsgodeus = E100#{#+#}#>#{#+#}#100

• Godsgodeucross = E100#{#+#}##100

• Godsgodeucubor = E100#{#+#}###100

• Godsgodeutope = E100#{#+#}#^#100

• Godsgodeu-arxitri = E100#{#+#}#{#+#}#100

• Godsgodeugahlah (Alternatively godsgodeu-arxihect) = E100#{#+#+1}#100

• Godsgodeugahcross = E100#{#+#+1}##100

• Godsgodeugahcubor = E100#{#+#+1}###100

• Godsgodeugahtope = E100#{#+#+1}#^#100

• Godsgodeugahularxitri = E100#{#+#+2}#3

• Godsgodeutethrathoth = E100#{#+#+2}#100

• Godsgodeupentacthulhum = E100#{#+#+3}#100

• Godsgotreusgahlah = E100#{#+#+#+1}#100

• Godsgotreusthratoth = E100#{#+#+#+2}#100

• Godsgotreuspentacthulhum = E100#{#+#+#+3}#100

• Godscrossgulus = E100#{##}#100

• Godscrossgahlah = E100#{##+1}#100

• Godscrossthrathoth = E100#{##+2}#100

• Godscrosspentacthulhum = E100#{##+3}#100

• Godscrossgodgulus = E100#{##+#}#100

• Godscrossgodeus = E100#{##+#+#}#100

• Godscrossgotreus = E100#{##+#+#+#}#100

• Godsdeucrossgulus = E100#{##+##}#100

• Godstreucrossgulus = E100#{##+##+##}#100

• Godscuborgulus = E100#{###}#100

• Godsterongulus = E100#{####}#100

• Godsdekongulus = E100#{#^10}#100

• Godstopegulus (Normally The centurion) = E100#{#^#}#100

• Godstopodeugulus = E100#{#^#*#^#}#100

• Godslattitopogulus = E100#{#^##}#100

• Godscubitopogulus = E100#{#^###}#100

• Gods-godgathor-gulus = E100#{#^#^#}#100

• Gods-gralgathor-gulus = E100#{#^#^##}#100

• Gods-godtothol-gulus = E100#{#^#^#^#}#100

• Gods-tethrathoth-gulus (Normally Super centurion) = E100#{#^^#}#100

• Gods-monster-giant-gulus = E100#{(#^^#)^(#^^#)^#}#100

• Gods-tethriterator-gulus = E100#{#^^#>#}#100

• Gods-tethracross-gulus = E100#{#^^##}#100

• Gods-tethratope-gulus = E100#{#^^#^#}#100

• Gods-tethrarxitri-gulus = E100#{#^^#^^#}#100

• Gods-pentacthulhum-gulus = E100#{#^^^#}#100

• Gods-hexacthulhum-gulus = E100#{#^^^^#}#100

• Gods-godsgodgulus-gulus (Alternatively godsarxitrigulus, Normally Ohmygosh-ohmygosh-ohmygooosh) = E100#{#{#}#}#100

• Godsarxitetgulus  (Normally Ohmygosh-ohmygosh-ohmygosh-ohmygooosh) = E100#{#{#{#}#}#}#100

• Godsarxipentgulus (Normally Ohmygosh-ohmygosh-ohmygosh-ohmygosh-ohmygooosh) = E100#{#{#{#{#}#}#}#}#100

• Godsarxideckgulus = E100#{{1}}#10

• Godsarxicosgulus = E100#{{1}}#20

• Godsarxitriangulus = E100#{{1}}#30

• Godsarxisarangulus = E100#{{1}}#40

• Godsarxipeningulus = E100#{{1}}#50

• Godsarxiexingulus = E100#{{1}}#60

• Godsarxiebdomingulus = E100#{{1}}#70

• Godsarxiogdongulus = E100#{{1}}#80

• Godsarxieneningulus = E100#{{1}}#90

• Godsarxihectgulus (Normally Blasphemorgulus) = E100#{{1}}#100

• Multi-blasphemorgulus = E100#{{2}}#100

• Power-blasphemorgulus = E100#{{3}}#100

• Blasphemortethragulus = E100#{{4}}#100

• Blasphemorpentacthulgulus = E100#{{5}}#100

• Boliath = E100#{{#}}#10

• Bolligog = E100#{{#}}#50

• Godsbodgulus = E100#{{#}}#100

• Blasphemorpopacthulgulus = E100#{{#}}#P where P is the world population right now

• Grand godsbodgulus = E100#{{#}}#100#2

• Godsbocrossgulus = E100#{{##}}#100

• Godsbotopegulus = E100#{{#^#}}#100

• Godsbo-tethrathoth-gulus = E100#{{#^^#}}#100

• Godsbo-godsgodgulus-gulus = E100#{{#{#}#}}#100

• Godsbo-godsbodgulus-gulus (Alternatively Godsdarxitrigulus) = E100#{{#{{#}}#}}#100 = E100{#, #, {#, #, #, 2}, 2}100

• Godsdarxitet = E100#{{#{{#{{#}}#}}#}}#100

• Godsdarxideck = E100#{{{1}}}#10

• Trlasphemorgulus = E100#{{{1}}}#100

• Godstrodgulus = E100#{{{#}}}#100

Warning: The next googolisms won't use an "official" notation, but rather, it'll use the Ascending-E Notation. If you don't know about it, you can look back.

• Ascended Googol (Normally Godgahlah) = E100(E[#]#)100

• Ascended Googolplex (Normally Godgathor) = E100(E[#]#{#}2)100

• Ascended Googolduplex (Normally Godtothol) = E100(E[#]#{#}3)100

• Ascended Googoltriplex (Normally Godtertol) = E100(E[#]#{#}4)100

• Ascended Grangol = E100(E[#]#{#}#)100

• Gralhecatathol = E100(E[#]##{#}100)100

• Thraelhecatathol = E100(E[#]###{#}100)100

• Goddenhecatathol = E100(E[#]#{#}101)100

• Goddohecatathol = E100(E[#]#{#}102)100

• Goddekahecatathol = E100(E[#]#{#}110)100

• God-icosahecatathol = E100(E[#]#{#}120)100

• Godduhecatathol = E100(E[#]#{#}200)100

• Godtruhecatathol = E100(E[#]#{#}300)100

• Godtetrihecatathol = E100(E[#]#{#}400)100

• Godpenhecatathol = E100(E[#]#{#}500)100

• Godchilliathol = E100(E[#]#{#}#)1,000

• Godmyriathol = E100(E[#]#{#}#)10,000

• Godmegatathol = E100(E[#]#{#}#)1,000,000

• Godgigatathol = E100(E[#]#{#}#)(E9)

• Goddialogiathol = E100(E[#]#{#}#)(E1#2)

• Godguppiathol = E100(E[#]#{#}#)(E20)

• Godgobiathol = E100(E[#]#{#}#)(E35)

• Godgogoliathol = E100(E[#]#{#}#)(E50)

• God-ogoliathol = E100(E[#]#{#}#)(E80)

• Godgoogliathol = E100(E[#]#{#}#)(E100)

• Gralgoogliathol = E100(E[#]##{#}#)(E100)

• Godgooglichimiathol = E100(E[#]#{#}#)(E1000)

• Godgrangolathol = E100(E[#]#{#}#)(E100#100)

• Godgreagolathol = E100(E[#]#{#}#)(E100#100#100)

• Godgugoldathol = E100(E[#]#{#}#)(E100##100)

• Godgugolthrathol = E100(E[#]#{#}#)(E100##100##100)

• Godthroogolathol = E100(E[#]#{#}#)(E100###100)

• Godtetroogolathol = E100(E[#]#{#}#)(E100####100)

• Goddektoogolathol = E100(E[#]#{#}#)(E100(E[#]#)10)

• Godgodgahlahathol = E100(E[#]#{#}#)(E100(E[#]#)100)

• Godgridgahlahathol = E100(E[#]#{#}#)(E100(E[#]##)100)

• Godgodgathorathol = E100(E[#]#{#}#)(E100(E[#]#{#}#)2)

• Godgodtotholathol = E100(E[#]#{#}#)(E100(E[#]#{#}#)3)

• Godgodtopolathol = E100(E[#]#{#}#)(E100(E[#]#{#}#)5)

• Godgoddekatholathol = E100(E[#]#{#}#)10#2

• Godgodhecatatholatholathol = E100(E[#]#{#}#)100#2

• Godgodgoogliatholathol = E100(E[#]#{#}#)(E100)#2

• Godgodgrangolatholathol = E100(E[#]#{#}#)(E100#100)#2

• Godgodgugoldatholathol = E100(E[#]#{#}#)(E100##100)#2

• Godgodgodgahlahatholathol = E100(E[#]#{#}#)1#3

• Godgodgodgathoratholathol = E100(E[#]#{#}#)2#3

• Godgodgoddekatholatholathol = E100(E[#]#{#}#)10#3

• Godgodgodhecatatholatholathol = E100(E[#]#{#}#)100#3

• Godgodgodgodgodhecatatholatholatholatholathol = E100(E[#]#{#}#)100#5

• Godgodgodgodgodgodgodgodgodgodhecatatholatholatholatholatholatholatholatholatholathol = E100(E[#]#{#}#)100#10

• Grangol-carta-ascengrangol = E100(E[#]#{#}#)100#100

• Greagol-carta-ascengrangol = E100(E[#]#{#}#)100#100#100

• Gugold-carta-ascengrangol = E100(E[#]#{#}#)100##100

• Godgahlah-carta-ascengrangol = E100(E[#]#{#}#)100(E[#]#)100

• Godgathor-carta-ascengrangol = E100(E[#]#{#}#)100(E[#]#{#}2)100

• Ascengrangol-by-deuteron = E100(E[#]#{#}#)100(E[#]#{#}#)100

• Ascengrangol-by-hyperion = E100(E[#]#{#}#)*#100

• Ascengrangol-by-godgahlah = E100(E[#]#{#}#)*(E[#]#)100

• Deutero-ascengrangol = E100(E[#]#{#}#)*(E[#]#{#}#)100

• Ascengrangolfact = E100(E[E[#]#{#}#]#)100

• Ascengrangolgridifact = E100(E[E[#]#{#}#]##)100

• Ascengrangol-ipso-godgahlah = E100(E[E[#]#{#}#](E[#]#))100

• Ascengrangol-ipso-godgathor = E100(E[E[#]#{#}#](E[#]#{#}2))100

• Ascengrangolduliath = E100(E[E[#]#{#}#](E[#]#{#}#))100

• Ascengrangoldeus = E100(E[E[#]#{#}#]#{#}#)100

• Ascengrangoltruce = E100(E[E[E[#]#{#}#]#{#}#]#{#}#)100

• Ascengrangolquad = E100(E[#]#{#}#)>#4

• Ascengrangolquid = E100(E[#]#{#}#)>#5

• Ascengrangoldeck = E100(E[#]#{#}#)>#10

• Ascengrangolicose = E100(E[#]#{#}#)>#20

• Ascengrangoliterator = E100(E[#]#{#}#)>#100

• Ascengrangoliteratordeus = E100(E[E[#]#{#}#)>#]#{#}#)>#100

• Ascengrangolgriditerator = E100(E[#]#{#}#)>##100

• Ascengrangolgodgahlahator = E100(E[#]#{#}#)>(E[#]#)100

• Ascengrangolgodgathorator = E100(E[#]#{#}#)>(E[#]#{#}2)100

• Ascengrangoldustaculator = E100(E[#]#{#}#)>(E[#]#{#}#)100

• Ascengrangoldustaculiterator = E100(E[#]#{#}#)>(E[#]#{#}#)>#100

• Ascengrangoldustaculgodgahlahator = E100(E[#]#{#}#)>(E[#]#{#}#)>(E[#]#)100

• Ascengrangoltristaculator = E100(E[#]#{#}##)3

• Ascengrangolpentastaculator = E100(E[#]#{#}##)5

• Ascengrangoldekastaculator = E100(E[#]#{#}##)10

• Ascengrangolcross = E100(E[#]#{#}##)100

• Ascengrangolitercross = E100(E[#]#{#}##)>#100

• Ascengrangoldustaculcross = E100(E[#]#{#}##)>(E[#]#{#}##)100

• Ascengrangolcubor = E100(E[#]#{#}###)100

• Ascended googoldex = E100(E[#]#{#}1{#}2)100

• Ascended googolplexidex = E100(E[#]#{#}2{#}2)100

• Ascended googolquintiplexidex = E100(E[#]#{#}6{#}2)100

• Ascended googoldeciplexidex = E100(E[#]#{#}11{#}2)100

• Ascended grangoldex = E100(E[#]#{#}#{#}2)100

• Ascended googoldudex = E100(E[#]#{#}1{#}2)100

• Ascended googoldeciplexidudex = E100(E[#]#{#}11{#}2)100

• Ascended grangoldudex = E100(E[#]#{#}#{#}3)100

• Ascended grangoldecidex = E100(E[#]#{#}#{#}11)100

• Ascended Greagol = E100(E[#]#{#}#{#}#)100

• Ascended Gigangol = E100(E[#]#{#}#{#}#{#}#)100

• Ascended Gorgegol = E100(E[#]#{#}#{#}#{#}#{#}#)100

• Ascended Gulgol = E100(E[#]#{#}#{#}#{#}#{#}#{#}#)100

• Ascended Gaspgol = E100(E[#]#{#}#{#}#{#}#{#}#{#}#{#}#)100

• Ascended Ginorgol = E100(E[#]#{#}#{#}#{#}#{#}#{#}#{#}#{#}#)100

• Ascended Gargantuul = E100(E[#]#{#}#{#}#{#}#{#}#{#}#{#}#{#}#{#}#)100

• Ascended Googondol = E100(E[#]#{#}#{#}#{#}#{#}#{#}#{#}#{#}#{#}#{#}#)100

• Ascended Googonkosol = E100(E[#]#{##}#)20

• Ascended Googontritol = E100(E[#]#{##}#)30

• Ascended Googonsartol = E100(E[#]#{##}#)40

• Ascended Googonpetol = E100(E[#]#{##}#)50

• Ascended Googonextol = E100(E[#]#{##}#)60

• Ascended Googoneptol = E100(E[#]#{##}#)70

• Ascended Googonogdol = E100(E[#]#{##}#)80

• Ascended Googonentol = E100(E[#]#{##}#)90

• Ascended Gugold = E100(E[#]#{##}#)100

• Ascended Graatagold = E100(E[#]#{##}#{#}#)100

• Ascended Gugolthra = E100(E[#]#{##}#{##}#)100

• Ascended Gugoltesla = E100(E[#]#{##}#{##}#{##}#)100

• Ascended Throogol = E100(E[#]#{###}#)100

• Ascended Tetroogol = E100(E[#]#{####}#)100

• Ascended Godgahlah (Alternatively deutero-ascended googol) = E100(E[#]#{#^#}#)100 = E100(E[#]#{E[#]#}#)100

• Deutero-ascended Grangol = E100(E[#]#{E[#]#{#}#}#)100

• Deutero-ascended Greagol = E100(E[#]#{E[#]#{#}#{#}#}#)100

• Deutero-ascended Gugold = E100(E[#]#{E[#]#{##}#}#)100

• Deutero-ascended Throogol = E100(E[#]#{E[#]#{###}#}#)100

• Trito-ascended Googol = E100(E[#]#{E[#]#{E[#]#}#}#)100

Extended Ascending-E Notation (xE+)

• Teterto-ascended Googol = E100/5

• Pepto-ascended Googol = E100/6

• Exto-ascended Googol = E100/7

• Epto-ascended Googol = E100/8

• Ogdo-ascended Googol = E100/9

• Ento-ascended Googol = E100/10

• Dekato-ascended Googol = E100/11

• Isosto-ascended Googol = E100/21

• Trianto-ascended Googol = E100/31

• Saranto-ascended Googol = E100/41

• Peninto-ascended Googol = E100/51

• Exinto-ascended Googol = E100/61

• Ebdominto-ascended Googol = E100/71

• Ogdonto-ascended Googol = E100/81

• Eneninto-ascended Googol = E100/91

• Ascaniongulus = E100/100

• Hecato-ascended Googol = E100/101

• Ascanionguluschime = E1,000/1,000

• Chillo-ascended Googol = E100/1,001

• Ascaniongulustoll = E10,000/10,000

• Ascaniongulusgong = E100,000/100,000

• Mega-ascended Googol = E100/1,000,001

• Ascaniongulus-sedeniad (Formerly ascaniongulus-sedenia) = E(10^16)/(10^16)

• Googol-ex-ascended googol = E100/(1+E100)

• Grangol-ex-ascended googol = E100/(1+E100#100)

• Greagol-ex-ascended googol = E100/(1+E100#100#100)

• Gorgegol-ex-ascended googol = E100/(1+E100##5)

• Googondol-ex-ascended googol = E100/(1+E100##10)

• Gugold-ex-ascended googol = E100/(1+E100##100)

• Gugolthra-ex-ascended googol = E100/(1+E100##100##100)

• Throogol-ex-ascended googol = E100/(1+E100###100)

• Tetroogol-ex-ascended googol = E100/(1+E100####100)

• Godgahlah-ex-ascended googol = E100/(1+E100#^#100)

• Gridgahlah-ex-ascended googol = E100/(1+E100#^##100)

• Godgathor-ex-ascended googol = E100/(1+E100#^#^#100)

• Godtothol-ex-ascended googol = E100/(1+E100#^#^#^#100)

• Tethrathoth-ex-ascended googol = E100/(1+E100#^^#100)

• Tethriterator-ex-ascended googol = E100/(1+E100#^^#>#100)

• Tethracross-ex-ascended googol = E100/(1+E100#^^##100)

• Tethratope-ex-ascended googol = E100/(1+E100#^^#^#100)

• Pentacthulhum-ex-ascended googol = E100/(1+E100#^^^#100)

• Hexacthulhum-ex-ascended googol = E100/(1+E100#^^^^#100)

• Godsgodgulus-ex-ascended googol = E100/(1+E100#{#}#100)

• Centurion-ex-ascended googol = E100/(1+E100#{#^#}#100)

• Ohmygosh-ohmygosh-ohmygooosh-ex-ascended googol = E100/(1+E100#{#{#}#}#100)

• Blasphemorgulus-ex-ascended googol = E100/(1+E100#{{1}}#100)

• Ascended-graatagold-ex-ascended googol = E100/(1+E100(E[#]#{##}#{#}#)100)

• Ascended-greegold-ex-ascended googol = E100/(1+E100(E[#]#{##}#{#}#{#}#)100)

• Ascended-gugolthra-ex-ascended googol = E100/(1+E100(E[#]#{##}#{##}#)100)

• Ascended-throogol-ex-ascended googol = E100/(1+E100(E[#]#{###}#)100)

• Two-ex-ascended-googol-ex-ascended googol = E100/(1+E100/3)

• Three-ex-ascended-googol-ex-ascended googol = E100/(1+E100/4)

• Five-ex-ascended-googol-ex-ascended googol = E100/(1+E100/6)

• Ten-ex-ascended-googol-ex-ascended googol = E100/(1+E100/11)

• Great and ascended googol (Alternatively grand ascaniongulus or ascaniongulus-minus-one-ex-ascended googol) = E100/100#2

• Hundred-ex-ascended-googol-ex-ascended googol = E100/(1+E100/101)

• Thousand-ex-ascended-googol-ex-ascended googol = E100/(1+E100/1,001)

• Myriad-ex-ascended-googol-ex-ascended googol = E100/(1+E100/10,001)

• Octad-ex-ascended-googol-ex-ascended googol = E100/(1+E100/100,000,001)

• Sedeniad-ex-ascended-googol-ex-ascended googol = E100/(1+E100/(1+E16))

• Googol-ex-ascended-googol-ex-ascended googol = E100/(1+E100/(1+E100))

• Ascended-googol-ex-ascended-googol-ex-ascended googol = E100/(1+E100/(1+E100/2))

• Two-ex-ascended-googol-ex-ascended-googol-ex-ascended googol = E100/(1+E100/(1+E100/3))

• Ten-ex-ascended-googol-ex-ascended-googol-ex-ascended googol = E100/(1+E100/(1+E100/11))

• Two-ex-great-and-ascended googol (Alternatively two-ex-grand ascaniongulus) = E100/100#3

• Three-ex-grand ascaniongulus = E100/100#4

• Five-ex-grand ascaniongulus = E100/100#6

• Ten-ex-grand ascaniongulus = E100/100#11

• Grangol-carta-ascaniongulus = E100/100#100

• Hundred-ex-grand ascaniongulus = E100/100#101

• Greagol-carta-ascaniongulus = E100/100#100#100

• Gugold-carta-ascaniongulus = E100/100##100

• Throogol-carta-ascaniongulus = E100/100###100

• Godgahlah-carta-ascaniongulus = E100/100#^#100

• Godgathor-carta-ascaniongulus = E100/100#^#^#100

• Tethrathoth-carta-ascaniongulus = E100/100#^^#100

• Pentacthulhum-carta-ascaniongulus = E100/100#^^^#100

• Godsgodgulus-carta-ascaniongulus = E100/100#{#}#100

• Blasphemorgulus-carta-ascaniongulus = E100/100#{{1}}#100

• Ascended-godgahlah-carta-ascaniongulus = E100/100(E[#]#{#^#}#)100

• Ascended-tethrathoth-carta-ascaniongulus = E100/100(E[#]#{#^^#}#)100

• Ascaniongulus-by-deuteron = E100/100/100

• Ascaniongulus-by-triton = E100/100/100/100

• Ascaniongulus-by-teterton = E100/#5

• Ascaniongulus-by-dekaton = E100/#11

• Ascaniongulus-by-isoston = E100/#21

• Ascanigoldgulus (Alternatively ascaniongulus-by-hyperion) = E100/#100

• Ascanithroogulus (Alternatively ascaniongulus-by-deutero-hyperion) = E100/##100

• Ascaniongulus-by-godgahlah = E100/(#^#)100

• Ascaniongulus-by-godgathor = E100/(#^#^#)100

• Ascaniongulus-by-tethrathoth = E100/(#^^#)100

• Ascaniongulus-by-pentacthulhum = E100/(#^^^#)100

• Ascaniongulus-by-ascended-gugold = E100/(E[#]#{##}#)100

• Deutero-ascaniongulus = E100//100

• Trito-ascaniongulus = E100///100

• Teterto-ascaniongulus = E100////100

• Pepto-ascaniongulus = E100/////100

• Dekato-ascaniongulus = E100/^#10

• Isosto-ascaniongulus = E100/^#20

• Trianto-ascaniongulus = E100/^#30

• Saranto-ascaniongulus = E100/^#40

• Peninto-ascaniongulus = E100/^#50

• Exinto-ascaniongulus = E100/^#60

• Ebdominto-ascaniongulus = E100/^#70

• Ogdonto-ascaniongulus = E100/^#80

• Eneninto-ascaniongulus = E100/^#90

• Ascaniongulfact = E100/^#100

• Ascaniongulgridifact = E100/^##100

• Ascaniongulus-ipso-godgahlah = E100/^#100

• Ascaniongulus-ipso-tethrathoth = E100/^#^^#100

• Dutetrated-ascaniongulus = E100/^/100

• Tritetrated-ascaniongulus = E100/^/^/100

• Terrible ascaniongulus = E100/^^#100

• Horrible ascaniongulus = E100/^^^#100

• Horrendous ascaniongulus = E100/^^^^#100

• Godsgorrendous ascaniongulus = E100/{#}#100

• Ascended Ascaniongulus = E100(E[/]/{/}/)100

• Deutero-ascended Ascaniongulus = E100(E[/]/{E[/]/{/}/}/)100

• Trito-ascended Ascaniongulus = E100(E[/]/{E[/]/{E[/]/{/}/}/}/)100

Hyper-Extended Ascending-E Notation (#xE+)

Warning: Since #xE+ and beyond are not defined yet, these numbers are ill-defined.

• Teterto-ascended Ascaniongulus = E100/_(2)5

• Pepto-ascended Ascaniongulus = E100/_(2)6

• Dekato-ascended Ascaniongulus = E100/_(2)11

• Isosto-ascended Ascaniongulus = E100/_(2)21

• Peninto-ascended Ascaniongulus = E100/_(2)51

• Ascanidiongulus = E100/_(2)100

• Ascended Ascanidiongulus = E100(E[/_(2)]/_(2){/_(2)}/_(2))100

• Ascanitriongulus = E100/_(3)100

• Ascanitetriongulus = E100/_(4)100

• Ascanipentiongulus = E100/_(5)100

• Ascanideckiongulus = E100/_(10)100

• Ascanihyperiongulus = E100/_(#)100

• Ascani-godgahlah-gulus = E100/_(#^#)100

• Ascani-godgathor-gulus = E100/_(#^#^#)100

• Ascani-tethrathoth-gulus = E100/_(#^^#)100

• Ascani-pentacthulhum-gulus = E100/_(#^^^#)100

• Ascani-ascended-gugold-gulus = E100/_(E[#]#{##}#)100

• Ascani-ascaniongulus-gulus (Alternatively Dustaculated-ascaniongulus) = E100/_(/)100

• Tristaculated-ascaniongulus = E100/_(/_(/))100

• Tetrastaculated-ascaniongulus = E100/_(/_(/_(/)))100

• Dekastaculated-ascaniongulus = E100/_(/_(/_(/_(/_(/_(/_(/_(/_(/)))))))))100

• Icosastaculated-ascaniongulus = E100/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(/)))))))))))))))))))100

• Triantastaculated-ascaniongulus = E100/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(.../_(/_(/_(/_(/_(/_(/_(/_(/_(/)))))))))...))))))))))100 with 30 /'s

• Terantastaculated-ascaniongulus = E100/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(.../_(/_(/_(/_(/_(/_(/_(/_(/_(/)))))))))...))))))))))100 with 40 /'s

• Penantastaculated-ascaniongulus = E100/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(.../_(/_(/_(/_(/_(/_(/_(/_(/_(/)))))))))...))))))))))100 with 50 /'s

• Exatastaculated-ascaniongulus = E100/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(.../_(/_(/_(/_(/_(/_(/_(/_(/_(/)))))))))...))))))))))100 with 60 /'s

• Eptatastaculated-ascaniongulus = E100/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(.../_(/_(/_(/_(/_(/_(/_(/_(/_(/)))))))))...))))))))))100 with 70 /'s

• Ogdatastaculated-ascaniongulus = E100/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(.../_(/_(/_(/_(/_(/_(/_(/_(/_(/)))))))))...))))))))))100 with 80 /'s

• Enenintastaculated-ascaniongulus = E100/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(.../_(/_(/_(/_(/_(/_(/_(/_(/_(/)))))))))...))))))))))100 with 90 /'s

• Hecatastaculated-ascaniongulus = E100/_(/_(/_(/_(/_(/_(/_(/_(/_(/_(.../_(/_(/_(/_(/_(/_(/_(/_(/_(/)))))))))...))))))))))100 with 100 /'s

Higher-E Notation (E.)

• Second Ascaniongulus (Alternatively Hecatastaculated-ascaniongulus) = E100[\2]100

• Dustaculated-second-ascaniongulus = E100[\2]_([\2])100

• Tristaculated-second-ascaniongulus = E100[\2]_([\2]_([\2]))100

• Pentastaculated-second-ascaniongulus = E100[\2]_([\2]_([\2]_([\2]_([\2]))))100

• Dekastaculated-second-ascaniongulus = E100[\2]_([\2]_([\2]_([\2]_([\2]_([\2]_([\2]_([\2]_([\2]_([\2])))))))))100

• Third ascaniongulus = E100[\3]100

• Fourth ascaniongulus = E100[\4]100

• Fifth ascaniongulus = E100[\5]100

• Sixth ascaniongulus = E100[\6]100

• Seventh ascaniongulus = E100[\7]100

• Eighth ascaniongulus = E100[\8]100

• Ninth ascaniongulus = E100[\9]100

• Tenth ascaniongulus = E100[\10]100

• Twentieth ascaniongulus = E100[\20]100

• Thirtieth ascaniongulus = E100[\30]100

• Fortieth ascaniongulus = E100[\40]100

• Fiftieth ascaniongulus = E100[\50]100

• Sixtieth ascaniongulus = E100[\60]100

• Seventieth ascaniongulus = E100[\70]100

• Eightieth ascaniongulus = E100[\80]100

• Nintieth ascaniongulus = E100[\90]100

• Hypered ascaniongulus (Alternatively Hundredth ascaniongulus) = E100[\#]100

• Di-hypered ascaniongulus = E100[\(#+#)]100

• Grid-hypered ascaniongulus = E100[\##]100

• Godgahlah-ranked-ascaniongulus = E100[\(#^#)]100

• Gridgahlah-ranked-ascaniongulus = E100[\(#^##)]100

• Godgathor-ranked-ascaniongulus = E100[\(#^#^#)]100

• Godgathorfact-ranked-ascaniongulus = E100[\(#^(#^#*#))]100

• Godgathordeus-ranked-ascaniongulus = E100[\(#^(#^#*#^#))]100

• Gralgathor-ranked-ascaniongulus = E100[\(#^#^##)]100

• Godtothol-ranked-ascaniongulus = E100[\(#^#^#^#)]100

• Tethrathoth-ranked-ascaniongulus = E100[\(#^^#)]100

• Tethriterator-ranked-ascaniongulus = E100[\(#^^#>#)]100

• Tethracross-ranked-ascaniongulus = E100[\(#^^##)]100

• Tethratope-ranked-ascaniongulus = E100[\(#^^#^#)]100

• Pentacthulhum-ranked-ascaniongulus = E100[\(#^^^#)]100

• Hexacthulhum-ranked-ascaniongulus = E100[\(#^^^^#)]100

• Godsgodgulus-ranked-ascaniongulus = E100[\(#{#}#)]100

• Ascended-gugold-ranked-ascaniongulus = E100[\(E[#]#{##}#)]100

• Deutero-ascended-googol-ranked-ascaniongulus = E100[\(E[#]#{E[#]#}#)]100

• Deuteranked Ascaniongulus = E100[\/]100

• Tritoranked Ascaniongulus = E100[\[\/]]100

• Tetertoranked Ascaniongulus = E100[\[\[\/]]]100

• Peptoranked Ascaniongulus = E100[\[\[\[\/]]]]100

• Dekatoranked Ascaniongulus = E100[\\]9

• The Dual Wield = E100[\\]100

• The Trial Wield = E100[\\\]100

• The Quadruple Wield = E100[\\\\]100

• The Quintuple Wield = E100[\\\\\]100

• The Dektuple Wield = E100[\\\\\\\\\\]100

• The Hyperuple Wield = E100[[\_(2)2]]100

• The Dual 2-wield = E100[[\_(2)\_(2)]]100

• The Trial 2-wield = E100[[\_(2)\_(2)\_(2)]]100

• The Quadruple 2-wield = E100[[[\_(3)2]]]4

• The Quintuple 2-wield = E100[[[\_(3)2]]]5

• The Dektuple 2-wield = E100[[[\_(3)2]]]10

• The Hyperuple 2-wield = E100[[[\_(3)2]]]100

• The Hyperuple 3-wield = E100[[[[\_(4)2]]]]100

• The Hyperwield = E100[\_(#)]100

• The Deuterhyperwield = E100[\_(#+#)]100

• The Gridihyperwield = E100[\_(##)]100

• Godgahlah-hyperwield = E100[\_(#^#)]100

• Godgathor-hyperwield = E100[\_(#^#^#)]100

• Tethrathoth-hyperwield = E100[\_(#^^#)]100

• Pentacthulhum-hyperwield = E100[\_(#^^^#)]100

• Godsgodgulus-hyperwield = E100[\_(#{#}#)]100

• Godsarxitrigulus-hyperwield = E100[\_(#{#{#}#}#)]100

• Ascended-throogol-hyperwield = E100[\_(E[#]#{###}#)]100

• Ascaniongulus-hyperwield = E100[\_(/)]100

• Dustaculated-hyperwield = E100[\_(\)]100

• Tristaculated-hyperwield = E100[\_(\_(\))]100

• Tetrastaculated-hyperwield = E100[\_(\_(\_(\)))]100

• Pentastaculated-hyperwield = E100[\_(\_(\_(\_(\))))]100

• Dekastaculated-hyperwield = E100[\_(\_(\_(\_(\_(\_(\_(\_(\_(\)))))))))]100

• Icosastaculated-hyperwield = E100[\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(\)))))))))))))))))))]100

• Triantastaculated-hyperwield = E100[\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(...\_(\_(\_(\_(\_(\_(\_(\_(\_(\)))))))))...))))))))))]100 with 30 \'s

• Sarantastaculated-hyperwield = E100[\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(...\_(\_(\_(\_(\_(\_(\_(\_(\_(\)))))))))...))))))))))]100 with 40 \'s

• Penantastaculated-hyperwield = E100[\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(...\_(\_(\_(\_(\_(\_(\_(\_(\_(\)))))))))...))))))))))]100 with 50 \'s

• Exantastaculated-hyperwield = E100[\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(...\_(\_(\_(\_(\_(\_(\_(\_(\_(\)))))))))...))))))))))]100 with 60 \'s

• Ebdomintastaculated-hyperwield = E100[\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(...\_(\_(\_(\_(\_(\_(\_(\_(\_(\)))))))))...))))))))))]100 with 70 \'s

• Ogdontastaculated-hyperwield = E100[\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(...\_(\_(\_(\_(\_(\_(\_(\_(\_(\)))))))))...))))))))))]100 with 80 \'s

• Enenintastaculated-hyperwield = E100[\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(...\_(\_(\_(\_(\_(\_(\_(\_(\_(\)))))))))...))))))))))]100 with 90 \'s

• The next level (Alternatively Hecatastaculated-hyperwield) = E100[\_(\_(\_(\_(\_(\_(\_(\_(\_(\_(...\_(\_(\_(\_(\_(\_(\_(\_(\_(\)))))))))...))))))))))]100 with 100 \'s

"Sleeping on the job gang" series

I've seen many people make interesting series of numbers, so I decided to make my own, too.

1. Dust = 0.0016

2. Locked Door = 19

3. Line to Circle = 60,112^π

4. Circle to Sphere = (Line to Circle)^12,932

5. Sphere to Sphessact = (Cricle to Sphere)^^^44

6. Sphesseract to Spenteract = (Sphere to Sphesseract){5914}56432

7. Spenteract to Spinfinity = f_ε1(Sphesseract to Spenteract)

8. Beyond Spinfinity = s(Spenteract to Spinfinity, (Sphesseract to Spenteract)^(Locked Door) {1,,,,,,,,,,,,,,,,...,,,,,,,,,,,,,,,2} 2) where there are Line to Circle commas in {}'s

9. Only 1% can guess the next letter = 420[69{1337}69]420 in Username5243's Array Notation

10. No one can reach pink = 69420(((1337)(420))(69))(42069) in Numbers in Brackets Notation (Notation created by YouTuber Guest)

11. This game is impossible = 420[420{69/69/69}420]420 in DeepLineMadom's Array Notation

12. Don't say the same thing as me, "Impossible" edition = {1337, 1337 [69 [420 ~ 1337] 420] 420} in Bird's Array Notation

13. Ultimate Absolute F.I.N.A.L godly E...N...D...I...N...G infinite ominous death screen = 6969[&&5] in Ampersand Notation

14. grangol*grangol M.E.T.A.C.H.E.S.S = Egrangol#^^^^#>(#^#^#*#^#####*#^#+#^###+###+#)grangol in Extended Cascading-E Notation

15. Error generator = {L666, X^3}_404,404 in BEAF

16. Copypaste.exe has stopped working = (Error generator)[(Error generator)[(Error generator)[...(Error generator)[(Error generator)[(Error generator)[This game is impossible]]]...]]] with Don't say the same thing as me "Impossible" edition []'s, in Copy Notation

17. This castle is collapsing = E(Spenteract to spinfinity)#{&###}#(Sphesseract to spenteract) in Collapsing-E Notation

18. Protect your number, keep it = (Line to circle)$[[0]_[0]] in Dollar function

19. A glass of infinity = 50,000![1]w(353)/[1(50)2] in Hyperfactorial Array Notation

20. Grahal-th grade = [10, 10 {1} Grahal] in Graham Array Notation

21. The step squad = 100(99)(98)(97)(96)(95)...(5)(4)3 in Hayden's Array Notation

22. The staircase of ascension = E100(E[#]#{E[#]#{E[#]#{E[#]#{...E[#]#{E[#]#{E[#]#{E[#]#{#^#}2}3}4}5...}96}97}98}99)100 in Ascending-E Notation

23. Don't trust everyone on an abandoned street = 666donttrusteveryoneonanabandonedstreet in Letter Notation

24. Still not fast enough = /0,0,Gooblol in Lightspeed Slash Notation

25. Gobbled up = #[[[@]]]{0:0:4}((66))*3 in Pound-Star Notation

26. Health Insurance = 3.16*10^4,942 in Scientific Notation

27. Turn off the refrigerator! = Q<10, 10, 0, 0, 100> in Quick Array Notation

28. Fast and furious = f_ω^6*9+ω^4*20(1337) in Fast-growing Hierarchy

29. Come on, it's not hard; it's just hardy = H_ω^ω+ω^3(40) in Hardy Hierarchy

30. Slow down! = g_BHO(69420) in Slow-growing Hierarchy, where BHO is the Bachmann-Howard Ordinal

31. It's expandal, not expansional = 2[2[2[...2[2[2[5]]]...]]] with Moser []'s, in Steinhaus-Moser Notation

32. Reuse your stuff = {Circle to Sphere, Beyond Spinfinity ///////////////////// Copypaste.exe has stopped working}*(Locked Door)+Dust

33. 'cause training season's over = Reuse your stuff^^^^^^^^^^^(Dust^(-1))

34. I may be crazy, don't mind me = ('cause training season's over){'cause training season's over}999999

35. You ain't got knows = {(I may be crazy, don't mind me), Circle to Sphere, 1, 1, 9}

36. Memories bring back you = {You ain't got knows, Slow down! (1) 4}

37. I see danger in your eyes = {Memories bring back you, (It's expandal, not expansional) (3)(3) 2}

38. Turi ip ip ip = {I see danger in your eyes, Reuse your stuff (0, 3) 2}

39. It's hard to breathe, but that's alright = {Turi ip ip ip, This castle is collapsing (((0, 1) 0, 1) 6, 5, 5) 2}

40. Time is barely on our side = X^^(Grahal-th grade) & (It's hard to breathe, but that's alright)

41. We are heroes tonight = {Time is barely on our side, 3 / 2}

42. We aren't pixels on a screen = {We are heroes tonight, Sphesseract to Spenteract / 2}

43. Your fingertips are drifting away = {We aren't pixels on a screen, Slow Down! /////// 352335}

44. Steady increasing the commas = {L2, 1}_(Your fingertips are drifting away, Bukuwaha)

45. I love it when you call me señorita = {LX, 4}_(Steady increasing the commas, The step squad)

46. Deep in the dark = {LLLLLLLLLL(X^^X), X}_(I love it when you call me señorita, A glass of infinity)

47. Hold tight, hold tight, hold tight = {L & L, 1}_(Deep in the dark, 69420)

48. On the dance floor = {{{L, L / 2}, 1}_(L, L), 1}_((Hold tight, hold tight, hold tight),(Hold tight, hold tight, hold tight))

49. I know where we can go = {{{...{{{{L, L / 2}, 1}_(L, L), 1}_(L, L), 1}_(L, L), 1...}_(L, L), 1}_(L, L), 1}_(On the dance floor, On the dance floor) where there are On the dance floor L's in total

50. Tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar tar! = Tar^I know where we can go(I know where we can go)

51. Wake up! = E44,435,622(E[#]#{####}#)44,435,622

52. It's time to go! = E44,435,622(E[#]#{E[#]#{###}#}#)44,435,622

53. Can you jump down by 44,435,622 steps? = E44,435,622/699

54. Of course, I can jump down by 44,435,622 steps! = E44,435,622/(Can you jump down by 44,435,622 steps?) = E44,435,622/699#2

55. WAIT, NO, I WAS KIDD- woah! = E44,435,622///44,435,622

56. Ok, now let's call a taxi and go to the airport. = E44,435,622(E[/]/{/}/)444,443,356,562,222

57. Taxi driver: That's 10$. = E44,435,622/_(2)44,435,622

58. Airport worker: It's 100$ per ticket, how many people? = E44,435,622/_(##)44,435,622

59. We'll go as 2 people. = E44,435,622/_(/)44,435,622

60. Enjoy! = E44,435,622/_(/_(/))44,435,622

61. Ok, let's go to the plane! = E44,435,622[\2]44,435,622

62. Pilot: We'll go in 60 seconds. = E44,435,622[\3]44,435,622

63. The flight started! = E44,435,622[\#]44,435,622

64. Hey! Look! It's a straight river! = E44,435,622[\/]44,435,622

65. Oh, we crossed the border! = E44,435,622[\\]44,435,622

66. Pilot: Some food will be served right now. Enjoy! = E44,435,622[\\\]44,435,622

67. Aaaaaahhh, we're crossing an ocean! = E44,435,622[[\_(2)2]]44,435,622

68. Pilot: We landed! = E44,435,622[\_(#)]44,435,622

69. Phew, we're back home, nice! = E44,435,622[\_(\)]44,435,622

70. HA! I reverted your edits! = (Wake up!)^(-1)

71. Haha, I'm not joking! = (It's time to go!)^(-2)

72. Then why are you laughing? = (Can you jump by 44,435,622 steps?)^(-5)

73. I'm laughing at you! XD = (Of course, I can jump by 44,435,622 steps!)^(-10)

74. Stop, you're nonsense. = (WAIT, NO, I WAS KIDD- woah!)^(-100)

75. Oh, I need to go for dinner. You lo- I mean you win :/ = (I know where we can go)^(-(10^100))

76. Wait, no, it's coming! = (Oh, I need to go for dinner. You lo- I mean you win :/)^10^10^100

77. AAAAAAAAHHHHHH ITS THE END OF THIS SER-*CONNECTION LOST* = ..."The largest number definable by using no more than "The largest number definable by using no more than "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol" symbols in some K("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") system in some K2("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 2-system in some K3("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 3-system ... in some K"The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"-system where the number t can be represented by one symbol" symbols in some K("The largest number definable by using no more than "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol" symbols in some K("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") system in some K2("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 2-system in some K3("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 3-system ... in some K"The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"-system where the number t can be represented by one symbol") system in some K2("The largest number definable by using no more than "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol" symbols in some K("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") system in some K2("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 2-system in some K3("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 3-system ... in some K"The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"-system where the number t can be represented by one symbol") 2-system in some K3("The largest number definable by using no more than "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol" symbols in some K("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") system in some K2("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 2-system in some K3("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 3-system ... in some K"The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"-system where the number t can be represented by one symbol") 3-system in some ... in some K"The largest number definable by using no more than "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol" symbols in some K("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") system in some K2("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 2-system in some K3("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 3-system ... in some K"The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"-system where the number t can be represented by one symbol"("The largest number definable by using no more than "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol" symbols in some K("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") system in some K2("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 2-system in some K3("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 3-system ... in some K"The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"-system where the number t can be represented by one symbol") "The largest number definable by using no more than "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol" symbols in some K("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") system in some K2("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 2-system in some K3("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 3-system ... in some K"The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"-system where the number t can be represented by one symbol"-system where the number "The largest number definable by using no more than "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol" symbols in some K("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") system in some K2("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 2-system in some K3("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") 3-system ... in some K"The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"("The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol") "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol"-system where the number "The largest number definable by using no more than Utter Oblivion symbols in some K(Utter Oblivion) system in some K2(Utter Oblivion) 2-system in some K3(Utter Oblivion) 3-system ... in some KUtter Oblivion(Utter Oblivion) Utter Oblivion-system where the number Utter Oblivion can be represented by one symbol" can be represented by one symbol" can be represented by one symbol"... Where there are oblivion layers

78. SLEEPJOBGANG1.EXE HAS STOPPED WORKING. PLEASE USE SLEEPJOBGANG2.EXE INSTEAD. = L(10, 100) where L(x, y) is the largest number definable by using no more than x symbols in some K(x) system in some K2(x) 2-system in some K3(x) 3-system in some ... in some Ky(x) y-system where the number x can be represented by one symbol

79. Class 0 gathering = 1+2+3+4+5+6 = 21

80. Class 1 gathering = (10^12-6^2+10^6+6)/2 = 500000499985 

81. Class 2 gathering = (10^(10^6*2)-10^12+10^10^6+10^6)/2 ≈ 5*101999999

82. Class 3 gathering = (10^(10^10^6*2)-10^(10^6*2)+10^10^10^6+10^10^6)/2

83. Class 4 gathering = (10^(10^10^10^6*2)-10^(10^10^6*2)+10^10^10^10^6+10^10^10^6)/2

84. Class 5 gathering = (10^(10^10^10^10^6*2)-10^(10^10^10^6*2)+10^10^10^10^10^6+10^10^10^10^6)/2

85. Tetration level gathering = ((10^^10^^10)^2-10^(10^10^10^10^6*2)+10^^10^^10+10^10^10^10^10^6)/2

86. Up-arrow notation level gathering = ((f_ω(f_3(10)))^2-(10^^10^^10)^2+f_ω(f_3(10))+10^^10^^10)/2

87. Linear omega level gathering = ((f_ω^2(f_3(10)))^2-(f_ω(f_3(10)))^2+f_ω^2(f_3(10))+f_ω(f_3(10)))/2

88. Quadratic omega level gathering = ((f_ω^3(f_3(10)))^2-(f_ω^2(f_3(10)))^2+f_ω^3(f_3(10))+f_ω^2(f_3(10)))/2

89. Polynomial omega level gathering = ((f_ω^ω(f_3(10)))^2-(f_ω^3(f_3(10)))^2+f_ω^ω(f_3(10))+f_ω^3(f_3(10)))/2

My power towers of 10's

These are inspired by Saibian's power towers of 10's.

Expanxis regiment

"Expanxis" is pronounced "eks-PANK-sis".

• Mono-expanxis (Normally ten) = 10{{1}}1 = 10

• Dia-expanxis (Nomally Tridecal) = 10{{1}}2 = 10{10}10

• Tria-expanxis (Normally Tridecalplex) = 10{{1}}3 = 10{10{10}10}10

• Tetra-expanxis (Normally Tridecalduplex) = 10{{1}}4 = 10{10{10{10}10}10}10

• Penta-expanxis (Normally Tridecaltriplex) = 10{{1}}5 = 10{10{10{10{10}10}10}10}10

• Hexa-expanxis = 10{{1}}6

• Hepta-expanxis = 10{{1}}7

• Octa-expanxis = 10{{1}}8

• Enna-expanxis = 10{{1}}9

• Deka-expanxis (Alternatively Dia-multiexpanxis or Monologia-expanxis) = 10{{1}}10 = {{2}}2

• Icosa-expanxis = 10{{1}}20

• Trianta-expanxis = 10{{1}}30

• Teranta-expanxis = 10{{1}}40

• Penanta-expanxis = 10{{1}}50

• Exata-expanxis = 10{{1}}60

• Eptata-expanxis = 10{{1}}70

• Ogdata-expanxis = 10{{1}}80

• Entata-expanxis = 10{{1}}90

• Hecta-expanxis (Normally Corporal) = 10{{1}}100