Googologisms

Here is a list of my most significant googologisms:

Bent Arrow Array Notation

My first serious notation! Very WIP and subject to change.

Bent Arrow Notation:

a = a

a↰b = b^a

a↰b↰c = b {c} a in Bowers’ operator notation, equates to b ^c a

a↰b↰c↰d =  b {b {b…{b {c} a}...a} a} a with d recursions, e.g. 2↰3↰4↰5 = 3{3{3{3{3{4}2}2}2}2}2 = 3{3{3{3{3^^^3}2}2}2}2 

a↰b↰c↰d↰e = b {b {b…{b {c} a}...a} a} a with d↰e recursions

a↰b↰c↰d↰e↰f = b {b {b…{b {c} a}...a} a} a with d↰e↰f recursions.

You might notice that the effectiveness of this recursion should end at 7 terms, but this will happen:

a↰b↰c↰d↰e↰f↰g↰h = b{b {b…{b {c} a}...a} a} a with d↰e↰f↰g↰h recursions.

We can also put multiple arrows in a row, like up-arrow notation:

a↰↰b = a↰a↰a↰a↰a↰a…↰a with b recursions

a↰↰b↰↰c = a↰↰b↰b↰b↰b↰b…↰b with b recursions

a↰↰↰b = a↰↰a↰↰a↰↰a…↰↰a with b recursions, and so on.

Basic Bent Arrow Array Notation (BBenAAN):

a[c]b = a↰cb

a[[c]]b = a[a[a…a[c]b…]b] with c recursions

a[[[c]]]b = a[[a[[...a[[c]]b…]]b]] with c recursions

a[c, d]b = a[c]db

a[c, d, e]b = a[c, d]a[c, d]a…[c, d]b with e recursions

a[c, d, e, f]b = same as above, but with e↰f recursions.

Reuse the recursion rule from basic expressions for any more terms.

Extended Bent Arrow Array Notation (XBenAAN):

a[c / d]b = a[c, c, c, c…,c]b with d recursions

a[c / d / e]b = a[c / d[d/e]e]b

a[c / d / e / f]b = a[c / d[d / e / f]e]b

We can then diagonalize upon this further by putting multiple slashes in a row:

a[c // d]b = a[c / c / c /...c]b with d recursions

a[c /// d]b = a[c // c // c //...c]b with d recursions.

Super-Extended Bent Arrow Array Notation (2XBenAAN):

a[c{e}d]b = a[c /ᵉ d]b where e is the amount of slashes

a[c{e, f}d]b = a[c{c[c{c...[c{e}d]...d}d]d}d]b with f recursions

a[c{e, f, g}d]b = a[c{c[c{c...[c{e, f}d]...d}d]d}d]a[c{c[c{c...[c{e, f}d]...d}d]d}d]...b with g repetitions.

Again, reuse recursion rules for basic expressions (e.g. 4 arguments in curly braces, or {e, f, g, h}, repeats a[c{c[c{c...[c{e}d]...d}d]d}d]...b g↰h times, and so on).

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This is all of the notation for now, but I'll create more of it later!

Number Naming System:

An alternate number-naming system I came up with to be less confusing than conventional naming system. Numbers are denoted by the prefix of the number of zeroes after first number, then the prefix which applies to the first number, then the suffix -illion (e.g. Siunillion, pronounced CY-un-illion, is one million).

Un = 1

Du = 2

Tre = 3

Qu = 4

Qi = 5

Si = 6

Se = 7

Ot = 8

On = 9

Des = 10

Undes = 11

and so on.