Googology Devlog

Finitial Stage 1 | Classics

Finitial Stage 1.0 - Ordinal Level 0 | MQG

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

Monero - q(1;0)

Dero - q(2;0)

[Basically all of Quantum Googology is here.]

Finitial Stage 1.1 - 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)

Finitial Stage 1.2 - 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

Finitial Stage 1.3 - 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

Finitial Stage 1.4 - 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

Finitial Stage 1.5 - 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

Finitial Stage 1.6 - Ordinal Level 6

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

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

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

Finitial Stage 1.7 - 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}

Finitial Stage 1.8 - 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}

Finitial Stage 1.9 - 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}

Finitial Stage 1.10 - 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}

Finitial Stage 1.11 - 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}

Finitial Stage 1.12 - 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}

Finitial Stage 1.13 - 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}

Finitial Stage 1.14 - 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}

Finitial Stage 1.15 - 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}

Finitial Stage 1.16 - 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}

Finitial Stage 1.17 - 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

Finitial Stage 1.18 - 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}

Finitial Stage 1.19 - 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}

Finitial Stage 1.20 - 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}

Finitial Stage 1.21 - 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}

Finitial Stage 1.22 - 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}

Finitial Stage 1.23 - Ordinal Level 23

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

Finitial Stage 1.24 - Ordinal Level 24

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

Finitial Stage 1.25 - Ordinal Level 25

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

Finitial Stage 1.26 - Ordinal Level 26

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

Finitial Stage 1.27 - Ordinal Level 27

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

Finitial Stage 1.28 - Ordinal Level 28

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

Finitial Stage 1.29 - Ordinal Level 29

Limit of BAN

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

Largornity - L @ 10

Finitial Stage 1.30 - 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)

Finitial Stage 1.31 - Ordinal Level 31

Tritar - Tar(3)

Dekotar - Tar(10)

Hektotar - Tar(100) - 100 C's

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

Finitial Stage 1.32 - 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

Finitial Stage 1.33 - 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))

Finitial Stage 1.34 - Ordinal Level 34

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

Finitial Stage 1.35 - Ordinal Level 35

Rayo's Number - Rayo(10^100)

Big Foot - FOOT^10(10^100)

Finitial Stage 1.36 - Ordinal Level 36

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

Finitial Stage 1.37 - Ordinal Level 37 (finite fictional googology)

Finity - ⧜

Finity plus one - ⧜+1

Finity plus two - ⧜+2

Finity plus finity - ⧜+⧜

Finity plus... finity - ⧜+⧜+...

Finitial Stage 1.38 - Ordinal Level 38 (finite fictional googology)

Second Finity - ⧜_2

Second Finity plus one - ⧜_2+1

Second Finity plus finity - ⧜_2+⧜

Second Finity plus second finity - ⧜_2+⧜_2

Second Finity plus... second finity - ⧜_2+⧜_2+...

Third Finity - ⧜_3

Fourth Finity - ⧜_4

Bifinity - ⧜_⧜

Trifinity - ⧜_⧜_⧜

Finitial Stage 1.39 - Ordinal Level 39 (finite fictional googology)

Eclipse - 〇

Eclipse plus one - 〇+1

Eclipse plus finity - 〇+⧜

Eclipse plus eclipse - 〇+〇

Second Eclipse - 〇_2

Pre-Infinite Null - 〇^1(0) - Enclosing the gap between finities and infinities...

Pre-Infinite_2 Null - 〇^1(〇^1(0))

Halved Pre-Infinite Null - 〇^2(0)

Thirds Pre-Infinite Null - 〇^3(0)

Slashed-One Pre-Infinity Null - 〇^[〇^1(0)](0)

100-10^-⧜% Infinite - 〇^[〇^[...](0)](0)

Near Infinite... / Broken Omega

Finitial Stage 1.40 - Ordinal Level 40

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

Omega plus one - ω+1

Omega plus two - ω+2

Omega times two - ω2

Omega times two plus one - ω2+1

Omega times two plus two - ω2+2

Omega times three - ω3

Finitial Stage 1.41 - Ordinal Level 41

Omega squared - ω^2

Omega to the Omega - ω^ω

Omega to the Omega squared - ω^ω^2

Omega to the Omega to the Omega - ω^ω^ω

Finitial Stage 1.42 - Ordinal Level 42

Epsilon Null - ε0

Finitial Stage 1.43 - Ordinal Level 43

Zeta Null - ζ0

Finitial Stage 1.44 - Ordinal Level 44

Eta Null - η0

Phi-Four Zero - φ4(0)

Finitial Stage 1.45 - Ordinal Level 45

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)

Phi-One-Quadruple-Zero - φ(1, 0, 0, 0, 0) [fictional]

Phi-One-Decuple-Zero - φ(1, 0, ... 0, 0) [10 zeros] [fictional]

Phi-One-Omegafold-Zero - φ(1, 0, ... 0, 0) [ω zeros] [fictional]

Finitial Stage 1.46 - Ordinal Level 46

Small Veblen Ordinal - ψ_0(Ω^Ω^ω)

Large Veblen Ordinal - ψ_0(Ω^Ω^Ω)

Finitial Stage 1.47 - Ordinal Level 47

Bachmann-Howard Ordinal - ψ_0(Ω_2)

Finitial Stage 1.48 - Ordinal Level 48

Church-Kleene Ordinal - ω1^CK

Finitial Stage 1.49 - Ordinal Level 49

First Uncountable Ordinal - ω1 / Aleph One - ℵ1

Finitial Stage 1.50 - Ordinal Level 50

Omega Fixed Point - θ

Worldly Cardinal

Hyper-Worldly Cardinal

Finitial Stage 1.51 - Ordinal Level 51

Inaccessible Cardinal - I

Downlifting Cardinal

Uplifting Cardinal

Mahlo Cardinal - M

Weakly Compact Cardinal - K

Finitial Stage 1.52 - Ordinal Level 52

First Indescribable Cardinal

Totally Indescribable Cardinal

Strong Uplifting Cardinal

Unfoldable Cardinal

Huge Cardinal

Finitial Stage 1.53 - Ordinal Level 53

Rank-Into-Rank Cardinals

Romsey Cardinal

Superstrong Cardinal

Wholeness Axioms

Finitial Stage 1.54 - Ordinal Level 54

0=1 Cardinal

Reinhardt Cardinal

Absolute Finity

Absolute Infinity - Cardinal Gap

Finitial Stage 1.55 - Ordinal Level 55 (extra before true standard FG)

Absolute Infinity - Ω - ???? [-0.25]

Omega Cross One - ω†1 (1-sort irreducible collection)

Finitial Stage 1.56 - Ordinal Level 56 (extra before true standard FG)

α-sort irreducibility

Finitial Stage 1.57 - Ordinal Level 57 (extra before true standard FG)

Lambda-Ordinal - Λ

ω-almost-wellordering

Finitial Stage 1.58 - Ordinal Level 58 (extra before true standard FG)

Omega-Lambda - ω-Λ

∞-almost-wellordering - E_0

Formalism-Inaccessible Number - F_0

Finitial Stage 1.59 - Ordinal Level 59 (extra before true standard FG)

First Unformalizable Number - K1

Finitial Stage 1.60 - Ordinal Level 60

Absolute Totality - A - ???? [0] = ❉(0)

[more to come]