Googology Devlog

Celestial Class 1 | Part 1

Ordinal Level 0 | MQG

Zero - 0 = ???? [-2]

Monero - q(1;0)

Dero - q(2;0)

[Basically all of Quantum Googology is here.]

Ordinal Level 1

One - 1 = ???? [-1] / (0)

Two - 2 / (0)(0)

Three - 3 / (0)(0)(0)

Ten - 10

One Hundred - 100

One Thousand - 1,000

One Million - 1,000,000 - z(1, 1)

Myllion - 100,000,000 - 10↑8

One Billion / One Milliard - 1,000,000,000 - 10↑9 - z(2, 1)

Ordinal Level 2

Dialogue / Ten Billion / Ten Milliard - 10↑10

Trillion / Billion [L] - 10↑12 - z(3, 1)

Byllion - 10↑16

Decillion / Quintilliard [L] - 10↑33 - z(10, 1)

Googol - 10↑100

Quintyllion - 10↑128

Centillion - 10↑303 - z(100, 1)

Googolchime - 10↑1,000

Millillion - 10↑3,003 - z(1, 2) / z(1,000, 1)

Googoltoll - 10↑10,000

Decimillillion / Myrillion - 10↑30,003

Centimillillion - 10↑300,003

Maximusmillion - 10↑1,000,000

Micrillion - 10↑3,000,003 - z(2, 2) / z(1,000,000, 1)

Trialogue - 10↑10↑10

Googolplex - 10↑10↑100

Pentalogue - 10↑10↑10↑10↑10 = 10↑↑5

Ordinal Level 3

Decker/Dekalogue - 10↑↑10

Doovol/Icosalogue - 10↑↑20

Giggol - 10↑↑100

Dialogicalogue - 10↑↑10↑10

Googol-stack - 10↑↑10↑100

Giggolplex - 10↑↑10↑↑100

Deka-taxis - 10↑↑↑10

Gaggol - 10↑↑↑100

Geegol - 10↑↑↑↑100

Tridecal - 10{10}10 = 10↑↑↑↑↑↑↑↑↑↑10 = 10[↑]10

Ordinal Level 4

Boogol - 10{100}10 = 10[↑]100

Bwoogol - 10{1,000}10 = 10[↑]1,000

Megalum - 10{1,000,000}10 = 10[↑]1,000,000

Googotri - 10{10↑100}10 = 10[↑]10↑100

Giggotri - 10{10↑↑100}10 = 10[↑]10↑↑100

Tridecalplex - 10{10{10}10}10 = 10[↑]10[↑]10

Boogolplex - 10{10{100}10}10 = 10[↑]10[↑]100

Ordinal Level 5

Dialogue-corporal - 10{{1}}10 = 10[↑]↑10

Graham's Number - G64 ≈ 3{{1}}65 ≈ 3[↑]↑65

Dialogue-borporal - 10{{2}}10 = 10[↑]↑↑10

Grand Tridecal - 10{{10}}10 = 10[↑][↑]10

Trendal-Tridecal - 10{{{10}}}10 = 10[↑][↑][↑]10

General / Tetradecal - {10, 10, 10, 10} = 10[↑↑]10

Troogol - {10, 10, 10, 100} = 10[↑↑]100

Ordinal Level 6

Dialogue-regicalmol - {10, 10, 1, 1, 2}

Pentadecal - {10, 10, 10, 10, 10}

Quadroogol - {10, 10, 10, 10, 100}

Ordinal Level 7

Iteral - {10, 10 [2] 2}

Goobol - {10, 100 [2] 2}

Boobol - {10, 10, 100 [2] 2}

Gootrol - {10, 100 [2] 3}

Gossol - {10, 10 [2] 100}

Ordinal Level 8

{no name currently} - {10, 10 [2] 1, 2}

Gissol - {10, 10 [2] 100, 2}

Mossol - {10, 10 [2] 10, 100}

Bossol - {10, 10 [2] 10, 10, 100}

Ordinal Level 9

Diteral - {10, 10 [2] 1 [2] 2}

Dubol - {10, 100 [2] 1 [2] 2}

Dossol - {10, 10 [2] 1 [2] 100}

Triteral - {10, 10 [2] 1 [2] 1 [2] 2}

Ordinal Level 10

Xappol - {10, 10 [3] 2}

Goxxol - {10, 100 [3] 2}

Grand Xappol - {10, 10 [3] 3}

Demperal - {10, 10 [3] 10}

Goxbooxol - {10, 100 [3] 100}

Dueli-Xappol - {10, 10 [3] 1 [3] 2}

Colossol - {10, 10 [4] 2}

Terossol - {10, 10 [5] 2}

Ordinal Level 11

Dimendecal - {10, 11 [1, 2] 2} / {10, 10 [11] 2}

Gomgather - {10, 100 [1, 2] 2}

Gongulus - {10, 101 [1, 2] 2}

Gingulus - {10, 100 [1, 3] 2}

Bongulus - {10, 100 [1, 1, 2] 2}

Ordinal Level 12

{no name currently} - {10, 10 [1 [2] 2] 2}

Giplexulus - {10, 100 [1 [2] 1 [2] 2] 2}

Boplexulus - {10, 100 [1 [3] 2] 2}

Goduplexulus - {10, 100 [1 [1, 2] 2] 2}

Ordinal Level 13

{no name currently} - {10, 10 [1 \ 2] 2}

Tethrathoth - ≈ {100, 49 [1 \ 2] 2}

Goppatoth - 10^^100 & 10 or ≈ {10, 51 [1 \ 2] 2}

Fish Number 5 - ≈ {63, 63, 2 [1 \ 2] 2}

Tethrafact - {100, 100 [2 \ 2] 2}

Tethraduliath - {100, 100 [1 [1 \ 2] 2 \ 2] 2}

Ordinal Level 14

{no name currently} - {10, 10 [1 \ 3] 2}

Terrible Tethrathoth - {100, 100 [1 \ 3] 2}

Tethriterator - {100, 100 [1 \ 1, 2] 2}

Tethrigriditerator - {100, 100 [1 \ 1, 1, 2] 2}

Tethrispatialator - {100, 100 [1 \ 1 [2] 2] 2}

Dustaculated-tethrathoth - {100, 100 [1 \ 1 [1 \ 2] 2] 2}

Ordinal Level 15

{no name currently} - {10, 10 [1 \ 1 \ 2] 2}

Tethracross - {100, 100 [1 \ 1 \ 2] 2}

Secundo-tethracross - {100, 100 [1 \ 1 \ 3] 2}

Tethritercross - {100, 100 [1 \ 1 \ 1, 2] 2}

Tethracubor - {100, 100 [1 \ 1 \ 1 \ 2] 2}

Ordinal Level 16

{no name currently} - {10, 10 [1 [2 ¬ 2] 2] 2}

Tethratope - {100, 100 [1 [2 ¬ 2] 2] 2}

Tethralattitope - {100, 100 [1 [3 ¬ 2] 2] 2}

Tethrarxitri - {100, 100 [1 [1 [1 \ 2] 2 ¬ 2] 2] 2}

Ordinal Level 17

{no name currently} - {10, 10 [1 [1 \ 2 ¬ 2] 2] 2}

Kungulus - ≈ {10, 100 [1 [1 \ 2 ¬ 2] 2] 2} or 10↑↑↑100 & 10

Pentacthuliterator - {100, 100 [1 [1 \ 2 ¬ 2] 1, 2] 2}

Pentacthulcross - {100, 100 [1 [1 \ 2 ¬ 2] 1 \ 2] 2}

Quadrunculus - ≈ {10, 100 [1 [1 \ 2 ¬ 2] 1 [1 \ 2 ¬ 2] 2] 2} or 10↑↑↑↑100 & 10

Golligog - {100, 49 [1 [2 \ 2 ¬ 2] 2] 2}

Humongulus - ≈ {10, 98 [1 [2 \ 2 ¬ 2] 2] 2} or 10{100}10 & 10

Blasphemorgulus - {100, 100 [1 [1 \ 3 ¬ 2] 2] 2}

Gonguldeus - 10{{1}}100 & 10

Generatrix/Tetradecatrix - {10, 10, 10, 10} & 10

Lineatrix - 10 & 10 & 10 ≈ {10, 10 [1 [1 \ 1, 2 ¬ 2] 2] 2}

TREE(3) - ≈ {100, 100 [1 [2 \ 1, 2 ¬ 2] 2] 2}

SSCG(3) - ≈ {100, 100 [1 [1 \ 1, 1, 2 ¬ 2] 1 [1 [3 \ 2 ¬ 2] 1 [3 \ 2 ¬ 2] 1 [3 \ 2 ¬ 2] 1 [3 \ 2 ¬ 2] 2] 2] 2}

Boobawamba - {10, 10, 100 (1) 2} & 10

Emperatrix - {10, 10 (1) 10} & 10

Ordinal Level 18

{no name currently} - {10, 10 [1 [1 ¬ 3] 2] 2}

{no name currently} - {10, 10 [1 [1 ¬ 4] 2] 2}

{no name currently} - {10, 10 [1 [1 ¬ 1, 2] 2] 2}

{no name currently} - {10, 10 [1 [1 ¬ 1 ¬ 2] 2] 2}

Ordinal Level 19

{no name currently} - {10, 10 [1 [1 [2 \3 2] 2] 2] 2}

Tetrakulus - 4 & 4 & 4 & 4 or {4, 4 / 2}

Pentakulus - 5 & 5 & 5 & 5 & 5 or {5, 5 / 2}

Dekulus - {10, 10 / 2}

Ordinal Level 20

{no name currently} - {10, 10 [1 [2 \1, 2 2] 2] 2}

The Whopper - {10, 100 / 2}

Hectakulus - {100, 100 / 2}

Iterotwix - {10, 10 (1) 2 / 2} ≈ {10, 10 [11] 10 [1 [2 \1, 2 2] 2] 2}

{no name currently} - {10, 10 [1 [2 \2, 2 2] 2] 2}

{no name currently} - {10, 10 [1 [2 \1, 3 2] 2] 2}

Ordinal Level 21

{no name currently} - {10, 10 [1 [2 \1, 1, 2 2] 2] 2}

{no name currently} - {10, 10 [1 [2 \1, 1, 3 2] 2] 2}

{no name currently} - {10, 10 [1 [2 \1, 1, 1, 2 2] 2] 2}

{no name currently} - {10, 10 [1 [2 \1, 1, 1, 1, 2 2] 2] 2}

Ordinal Level 22

{no name currently} - {10, 10 [1 [2 \1 [2] 2 2] 2] 2}

{no name currently} - {10, 10 [1 [2 \1 [2] 1 [2] 2 2] 2] 2}

{no name currently} - {10, 10 [1 [2 \1 [3] 2 2] 2] 2}

{no name currently} - {10, 10 [1 [2 \1 [1, 2] 2 2] 2] 2}

{no name currently} - {10, 10 [1 [2 \1 [1 [2] 2] 2 2] 2] 2}

Ordinal Level 23

{no name currently} - {10, 10 [1 [2 \1 [1 \ 2] 2 2] 2] 2}

Ordinal Level 24

{no name currently} - {10, 10 [1 [2 \1 \ 2 2] 2] 2}

Ordinal Level 25

{no name currently} - {10, 10 [1 [2 \1 \ 3 2] 2] 2}

Ordinal Level 26

{no name currently} - {10, 10 [1 [2 \_(1 [2 \_(2) 2] 2) 2] 2] 2}

Ordinal Level 27

{no name currently} - {10, 10 [1 [2 \_(1 \_(2) 2) 2] 2] 2}

Ordinal Level 28

{no name currently} - {10, 10 [1 [2 \_(1 \_(1 \ 2) 2) 2] 2] 2}

Ordinal Level 29

Limit of BAN

Mirongualith - {L,X+1}_(10, 100)

Largornity - L @ 10

Ordinal Level 30

Reversed Triakulus - {3, 3 \ 2}

Big Bukuwaha - {100, 100 B 2} (Bukuwaha was {100, 100 A 2})

Bongo Bukuwaha - {100, 100 C 2}

Limit of BEAF - s(10, 100{1 {1 {1,,,, 2} 2,,,, 2} 1, 2} 2)

Ordinal Level 31

Tritar - Tar(3)

Dekotar - Tar(10)

Hektotar - Tar(100) - 100 C's

Unintar - Tar(Tar(3)) - Tar(3) C's

Ordinal Level 32

Loader’s Number - D^5(99)

Bashicu Matrix Number - f_Limit of BMS(10)

Yudkowsky’s Number - The current largest computable number yet

Ordinal Level 33

1918th Busy Beaver- Σ(1,918)

1919th Busy Beaver- Σ(1,919)

2020th Busy Beaver- Σ(2,020)

1919th 1-stack Busy Beaver - Σ(Σ(1,919))

One Millionth Xi Function - Ξ(1,000,000)

Rayo's Number - Rayo(10^100)

Big Foot - FOOT^10(10^100)

Ordinal Level 34

Oblivion - The Largest Number Defined Using No More Than A Kungulus Symbols

Utter Oblivion - The Largest Number Defined Using No More Than An Oblivion Symbols

Ultimate Oblivion - The Largest Number Defined Using No More Than An Utter Oblivion Symbols

Absolute Oblivion - The Oblivion that ends all Oblivions, which is defined using more than True Oblivion rulesets that has Absolute Oblivion minus one symbols each. It is permanently ill-defined and increases overtime.

Sam's Number - An inside joke within the googology community as an example of lazy and poorly defined googology.

Crouton

Croutonillion

Ordinal Level 35

Infinity - ∞ / Aleph Null - ℵ0 / Omega - ω / ???? [-0.5] | (0)(1)

Omega plus one - ω+1

Omega times two - ω2

Ordinal Level 36

Omega squared - ω^2

Ordinal Level 37

Epsilon Null - ε0

Epsilon Omega - εω

Epsilon Epsilon Null - εε0

Ordinal Level 38

Zeta Null - ζ0

Ordinal Level 39

Eta Null - η0

Ordinal Level 40

Gamma Null / Feferman-Schütte Ordinal - Γ0

Phi-One-One-Zero - φ(1, 1, 0)

Phi-One-Zero-Zero-Zero / Ackermann Ordinal - φ(1, 0, 0, 0)

Ordinal Level 41

Small Veblen Ordinal - ψ0(Ω^Ω^ω)

Large Veblen Ordinal - ψ0(Ω^Ω^Ω)

Ordinal Level 42

Bachmann-Howard Ordinal - ψ0(Ω_2)

Ordinal Level 43

Church-Kleene Ordinal - ω1^CK

Ordinal Level 44

First Uncountable Ordinal - ω1 / Aleph One - ℵ1

Ordinal Level 45

Omega Fixed Point - θ

Aleph Fixed Point

Beth One - ℶ1 

Worldly Cardinal

Hyper-Worldly Cardinal

Ordinal Level 46

Inaccessible Cardinal - I

Hyper-Inaccessible Cardinal - I(1,0,0)

Mahlo Cardinal - M

Weakly Compact Cardinal - K

Ordinal Level 47

First Indescribable Cardinal

Strong Uplifting Cardinal

Woodin Cardinal

Ramsey Cardinal

Huge Cardinal

Ordinal Level 48

Rank-Into-Rank Cardinals

Measureable Cardinal

Superstrong Cardinal

Ordinal Level 49

0=1 Cardinal

Axiom Limits

Absolute Finity

Absolute Infinity - Cardinal Gap

Ordinal Level 50 / Rustinal Level 11

Absolute Infinity - Ω - ???? [0] = ❉(0)

Absolute Infinity plus One - Ω+1

Absolute Infinity times Two - Ωx2

Absolute Infinity to the Absolute Infinity - Ω↑Ω

Absolute Infinity tetrated to Absolute Infinity - Ω↑↑Ω

Omega-Absolute Infinity

Epsilon Absolute Infinity

Inaccessible Absolute Infinity

Rustinal Level 12

Absolute One Infinity - Ω_1

Absolute Dulayer Infinity - Ω_Ω

Absolute Decilayer Infinity - Ωx10

Rustinal Level 13

Absolute Everything (Double-Stack Absolute Infinity) - ΩxΩ

Triplestack Absolute Infinity - ΩxΩxΩ

Decuple-Stack Absolute Infinity - Ωxx10

Double-Dustack Absolute Infinity - ΩxxΩ

Triple-Dustack Absolute Infinity - ΩxxΩxxΩ

Decuple-Dustack Absolute Infinity - Ωxxx10

Double-Trustack Absolute Infinity - ΩxxxΩ

Double-Decistack Absolute Infinity - ΩxX10

Rustinal Level 14

Absolutely Infinity Universe - ΩxXΩ

(alternate names: Double-Superstack Absolute Infinity / Absolutely Infinity One-x-One-X-Double-Stack)

Triple-Superstack Absolute Infinity - ΩxXΩxXΩ

Double-Supermonstack Absolute Infinity - ΩxXxΩ

Double-Superdustack Absolute Infinity - ΩxXxxΩ

Double-Superdecistack Absolute Infinity - ΩxXxX10

Double-Megastack Absolute Infinity - ΩxXxXΩ 

Double-Gigastack Absolute Infinity - ΩxXxXxXΩ

Double-Quettastack Absolute Infinity - ΩxXX10

Absolutely Infinity One-x-Two-X-Double-Stack - ΩxXXΩ

Absolutely Infinity Threefold-X-Stack - ΩxXXΩ / ΩxXχΩ / ΩxX(X3)Ω

Absolutely Infinity Fourfold-X-Stack - ΩxXXXΩ / ΩxXχЖΩ / ΩxX(X3)(X4)Ω

Absolutely Infinity Fivefold-X-Stack - ΩxXχЖ𝔁Ω / ΩxX(X3)(X4)(X5)Ω

Absolutely Infinity Sixfold-X-Stack - ΩxXχЖ𝔁𝓧Ω / ΩxX(X3)(X4)(X5)(X6)Ω = Ω(xX...)6

Absolutely Infinity Sevenfold-X-Stack - ΩxXχЖ𝔁𝓧𝕩Ω / ΩxX(X3)(X4)(X5)(X6)(X7)Ω = Ω(xX...)7

Absolutely Infinity Eightfold-X-Stack - ΩxXχЖ𝔁𝓧𝕩𝕏Ω / ΩxX(X3)(X4)(X5)(X6)(X7)(X8)Ω = Ω(xX...)8

Absolutely Infinity Ninefold-X-Stack - ΩxXχЖ𝔁𝓧𝕩𝕏𝖝Ω / ΩxX(X3)(X4)(X5)(X6)(X7)(X8)(X9)Ω = Ω(xX...)9

Absolutely Infinity Tenfold-X-Stack - Ω(xX...)10 / ΩxXχЖ𝔁𝓧𝕩𝕏𝖝𝖃Ω / ΩxX(X3)(X4)(X5)(X6)(X7)(X8)(X9)(X10)Ω

Rustinal Level 15

Absolutely Infinity Multiverse(Double-Pilestack Absolute Infinity / Absolutely Infinity Pile-Double-Stack) - Ω(xX...)Ω

Absolutely Infinity Double Dupilestack - Ω(xX...)(xX...)Ω

Double-Decipilestack Absolute Infinity - Ω(xX...)^x 10

Absolutely Infinity Double One-x-Pilestack - Ω(xX...)^x Ω

Absolutely Infinity Double Two-x-Pilestack - Ω(xX...)^xx Ω

Absolutely Infinity Double One-x-One-X-Pilestack - Ω(xX...)^xX Ω

Absolutely Infinity Double Dilestack - Ω(xX...)^(xX...) Ω

Rustinal Level 16

Absolutely Infinity Double Uperstack - Ω{xX...}Ω = ΩIxX...I2

Absolutely Infinity Double Complexstack - Ω[xX...]Ω = ΩIxX...I3

Absolutely Infinity Double Everstack - Ω/xX.../Ω = ΩIxX...I4

Absolutely Infinity Double Neverstack/Quinarystack - Ω|xX...|Ω = ΩIxX...I5

Absolutely Infinity Double Denarystack - ΩIxX...I10

Rustinal Level 17

Absolutely Infinite-finity (Absolutely Infinity Double Colossalstack) - ΩIxX...IΩ

Absolutely Infinity Double Pilecolossalstack - Ω(IxX...I)Ω

Absolutely Infinity Double Upercolossalstack - Ω{IxX...I}Ω

Absolutely Infinity Double One-x-Colossalstack - ΩIxX...I^x Ω

Absolutely Infinity Double Copilossalstack - ΩI(xX...)IΩ

Absolutely Infinity Double Bolossalstack - ΩIIxX...IIΩ

Rustinal Level 18

Absolutely Infinity Double Colomonalstack - Ω.IxX...I.Ω

Absolutely Infinity Double Bolomonalstack - Ω.IIxX...II.Ω

Absolutely Infinity Double Colobonalstack - Ω..IxX...I..Ω

Absolutely Infinity Double Colodeconalstack - Ω<...IxX...I...>_x 10

Absolutely Infinity Double Galacticstack - Ω<...IxX...I...>_x Ω

Absolutely Infinity Double Kiloverstack - Ω<...IxX...I...>_<...IxX...I...>_x Ω

Absolutely Infinity Double Teraverstack - ΩSx5

Absolutely Infinity Double Quettaverstack - ΩSx11

Rustinal Level 19

Absolute Super Everything - ΩSxΩ

Absolutely Super Infinity, Infinity Stack - ΩSx,xΩ

Absolute Duo-Super Everything - ΩSx,SxΩ

Absolute Decio-Super Everything - ΩSxx10

Absolutely Super Dustack Infinity - ΩSxxΩ

Absolutely Super Decistack Infinity - ΩSxX10

Absolutely Super Infinity Universe(Absolutely Super Superstack Infinity) - ΩSxXΩ

Absolutely Super Infinity Multiverse(Absolutely Super Infinity Pilestack) - ΩS(xX...)Ω

Absolutely Super Infinity Teraverstack - ΩMx5

Absolute Mega Everything - ΩMxΩ = Ω[3]➳xΩ

Absolute Giga Everything - ΩGxΩ = Ω[4]➳xΩ

Rustinal Level 20

Absolute Supi Everything - Ω[1,2]➳xΩ = Ω[Ω]➳xΩ

Absolute Supi-Super Everything - Ω[2,2]➳xΩ

Absolute Meji Everything - Ω[1,3]➳xΩ = Ω[Ω,2]➳xΩ

Absolute Sutria Everything - Ω[1,[1,2]]➳xΩ = Ω[1,Ω]➳xΩ

[more to come]