User:Numspan33/sandbox

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This is a list of googolisms in ascending order.

This page (the main list) lists the more notable googolisms on each class; click the "More..." link at the end of each section to see more googolisms in that class.
Googolisms in bold are numbers with peer-reviewed source.
Googolisms in italics are ill-defined and their placement within this page is reflective of their intended value, assuming them to be well-defined. This list contains ill-defined large numbers, e.g. BEAF numbers beyond tetrational arrays, BIG FOOT, Little Bigeddon, Sasquatch, Oblivion, Utter Oblivion, and large numbers whose well-definedness is not known, e.g. large numbers defined by Taranovsky's ordinal notation and Bashicu matrix number with respect to Bashicu matrix system version 2.3.

Class 0 (0 - 6)

Name	Value	Approximation (Fast-growing hierarchy)
Zero	0	N/A
Googolminex	$10^{-(10^{100})}$ or 1/googolplex	N/A
Googol-minutia	$10^{-100}$ or 1/googol	N/A
One	1	f₀(0)
Two	2	f₀(1)
Three	3	f₀(2)
Four	4	f₀(3)
Five	5	f₀(4)
Six	6	f₀(5)

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Class 1 (7 - 1,000,000)

Name	Value	Approximation (Fast-growing hierarchy)
Seven	7	f₀(6)
Eight	8	f₀(7)
Nine	9	f₀(8)
Ten	10	f₁(5)
Dozen	12	f₁(6)
Hundred	100 (10²)	f₁(50)
Eleventy	110	f₁(55)
Twelfty (or long hundred)	120	f₁(60)
Gross	144 (12²)	f₁(72)
Baker's gross	169 (13²)	f₂(5)
Poulter's gross	196 (14²)	f₁(98)
Short ream	480	f₂(6)
Ream	500	f₂(6)
Beast number	666	f₂(7)
Thousand / Niloogol	1,000 (10³)	f₂(7)
Great gross	1,728 (12³)	f₂(8)
Great Baker's gross	2,197 (13³)	f₂(8)
Poulter's great gross	2,744 (14³)	f₂(8)
Myriad	10,000	f₂(10)
Lakh	100,000	f₂(13)

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Class 2 (1,000,000 - $10^{1,000,000}$)

Name	Value	Approximation (Fast-growing hierarchy)
Million	1,000,000	f₂(16)
Crore	10,000,000	f₂(19)
Myllion	100,000,000	f₂(22)
Billion(S)^[1] / Milliard	1,000,000,000	f₂(25)
Dialogue	10¹⁰	f₂(29)
Trillion(S) / Billion(L)	10¹²	f₂(35)
Quadrillion(S) / Billiard	10¹⁵	f₂(45)
Byllion	10¹⁶	f₂(48)
Quintillion(S) / Trillion(L)	10¹⁸	f₂(54)
Guppy	10²⁰	f₂(61)
Sextillion(S) / Trilliard	10²¹	f₂(64)
Avogadro's number	6.02214076*10²³	f₂(73)
Septillion(S) / Quadrillion(L)	10²⁴	f₂(74)
Octillion(S) / Quadrilliard	10²⁷	f₂(83)
Nonillion(S) / Quintillion(L)	10³⁰	f₂(93)
Belphegor's prime	~1.00000000000007*10³⁰	f₂(93)
Tryllion	10³²	f₂(100)
Decillion(S) / Quintilliard	10³³	f₂(103)
Undecillion(S) / Sextillion(L)	10³⁶	f₂(113)
Duodecillion(S) / Sextilliard	10³⁹	f₂(123)
Tredecillion(S) / Septillion(L)	10⁴²	f₂(133)
Quattuordecillion(S) / Septilliard	10⁴⁵	f₂(143)
Quindecillion(S) / Octillion(L)	10⁴⁸	f₂(151)
Lcillion / Gogol	10⁵⁰	f₂(159)
Sexdecillion(S) / Octilliard	10⁵¹	f₂(162)
Septendecillion(S) / Nonillion(L)	10⁵⁴	f₂(171)
Octodecillion(S) / Nonilliard	10⁵⁷	f₂(182)
Novemdecillion(S) / Decillion(L)	10⁶⁰	f₂(192)
Vigintillion(S) / Decilliard	10⁶³	f₂(202)
Muryoutaisuu	10⁶⁸	f₂(219)
Eddington number	1362²⁵⁶ ~ 1.574772413627510⁷⁹	f₂(256)
Ogol	10⁸⁰	f₂(258)
Trigintillion(S)	10⁹³	f₂(301)
Googol	10¹⁰⁰	f₂(323)
Shannon number	10¹²⁰	f₂(390)
Quadragintillion(S)	10¹²³	f₂(400)
Googolex	120⁶⁰ ~ 5.6347514353165*10¹²⁴	f₂(405)
Quinquagintillion(S)	10¹⁵³	f₂(499)
Trigintillion(L)	10¹⁸⁰	f₂(589)
Sexagintillion(S)	10¹⁸³	f₂(599)
Number of Planck volumes in the observable universe	~4.6*10¹⁸⁵	f₂(607)
Gargoogol	10²⁰⁰	f₂(656)
Septuagintillion(S)	10²¹³	f₂(698)
Hundertime	4.71193079990*10²¹⁹	f₂(721)
Googoc	200¹⁰⁰ ~ 1.2676506002282*10²³⁰	f₂(754)
Quadragintillion(L)	10²⁴⁰	f₂(787)
Octogintillion(S)	10²⁴³	f₂(797)
Nonagintillion(S)	10²⁷³	f₂(897)
Quinquagintillion(L)	10³⁰⁰	f₂(996)
Centillion(S)	10³⁰³	f₂(997)
Sexagintillion(L)	10³⁶⁰	f₂(1,185)
Primo-vigesimo-centillion(S)	10³⁶⁶	f₂(1,205)
Faxul	200! ~ 7.88657867364*10³⁷⁴	f₂(1,235)
Septuagintillion(L)	10⁴²⁰	f₂(1,384)
Octogintillion(L)	10⁴⁸⁰	f₂(1,584)
Googocci	402²⁰¹ ~ 2.814729533583*10⁵²³	f₂(1,728)
Nonagintillion(L)	10⁵⁴⁰	f₂(1,783)
Centillion(L)	10⁶⁰⁰	f₂(1,982)
Ducentillion(S)	10⁶⁰³	f₂(1,992)
Primo-vigesimo-centillion(L)	10⁷²⁶	f₂(2,400)
Trecentillion(S)	10⁹⁰³	f₂(2,988)
Googolchime	10^1,000	f₂(3,310)
Quadringentillion(S)	10^1,203	f₂(3,984)
Quingentillion(S)	10^1,503	f₂(4,981)
Sescentillion(S)	10^1,803	f₂(5,977)
Septingentillion(S)	10^2,103	f₂(6,973)
Octingentillion(S)	10^2,403	f₂(7,970)
Nongentillion(S)	10^2,703	f₂(8,966)
Millillion(S)	10^3,003	f₂(9,962)
Decyllion	10^4,096	f₂(13,592)
Millillion(L)	10^6,000	f₂(19,917)
Googoltoll	10^10,000	f₂(33,204)
Myrillion/Decimillillion(S)	10^30,003	f₂(99,650)
Hitchhiker's number	2^267,709 ~ 2.748585232104986*10^80,588	f₂(f₂(14))
Googolgong	10^100,000	f₂(f₂(15))
Centimillillion(S)	10^300,003	f₂(f₂(16))

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Class 3 ($10^{1,000,000} - 10^{10^{1,000,000}}$)

Name	Value	Approximation (fast-growing hierarchy)
Maximusmillion	10^1,000,000	f₂(f₂(17))
Milli-millillion(S)	10^3,000,003	f₂(f₂(19))
Vigintyllion	10^4,194,304	f₂(f₂(19))
Milli-millillion(L)	10^6,000,000	f₂(f₂(20))
Largest known prime	2^82,589,933-1 ~ 1.488944*10^24,862,047	f₂(f₂(22))
Nanillion	10^{3,000,000,003}	f₂(f₂(28))
Trialogue	10^10¹⁰	f₂(f₂(30))
Ballium's number	~ 2.03542*10^{138,732,019,349}	f₂(f₂(33))
Picillion	10^3*10¹²+3	f₂(f₂(37))
Nirabhilapya nirabhilapya parivarta	$10^{7 \times 2^{122}}$	f₂(f₂(37))
Femtillion	10^3*10¹⁵+3	f₂(f₂(48))
Attillion	10^3*10¹⁸+3	f₂(f₂(57))
Guppyplex	10^10²⁰	f₂(f₂(63))
Zeptillion	10^3*10²¹+3	f₂(f₂(67))
Yoctillion	10^3*10²⁴+3	f₂(f₂(76))
Xonillion	10^3*10²⁷+3	f₂(f₂(86))
Vecillion	10^3*10³⁰+3	f₂(f₂(96))
Mecillion	10^3*10³³+3	f₂(f₂(106))
Duecillion	10^3*10³⁶+3	f₂(f₂(116))
Trecillion	10^3*10³⁹+3	f₂(f₂(125))
Tetrecillion	10^3*10⁴²+3	f₂(f₂(135))
Icosillion	10^3*10⁶⁰+3	f₂(f₂(195))
Doppelgängion	10^10⁶⁸	f₂(f₂(220))
Triacontillion	10^3*10⁹⁰+3	f₂(f₂(294))
Googolplex	10^10¹⁰⁰	f₂(f₂(325))
Gargoogolplex	googolplex² = 10^2*10¹⁰⁰	f₂(f₂(326))
Googolbang	(10¹⁰⁰)! ~ 10^{9.957*10¹⁰¹}	f₂(f₂(332))
Tetracontillion	10^{3*10¹²⁰+3}	f₂(f₂(393))
Pentacontillion	10^{3*10¹⁵⁰+3}	f₂(f₂(492))
Hexacontillion	10^{3*10¹⁸⁰+3}	f₂(f₂(592))
Heptacontillion	10^{3*10²¹⁰+3}	f₂(f₂(691))
Octacontillion	10^{3*10²⁴⁰+3}	f₂(f₂(791))
Ennacontillion	10^{3*10²⁷⁰+3}	f₂(f₂(890))
Hectillion	10^{3*10³⁰⁰+3}	f₂(f₂(989))
Ecetonplex	10^10³⁰³	f₂(f₂(998))
Kilofaxul	(200!)! ~ 10^10³⁷⁹	f₂(f₂(1245))
Dohectillion	10^{3*10⁶⁰⁰+3}	f₂(f₂(1985))
Triahectillion	10^{3*10⁹⁰⁰+3}	f₂(f₂(2981))
Googolplexichime	10^{10^1,000}	f₂(f₂(3311))
Tetrahectillion	10^{3*10^1,200+3}	f₂(f₂(3977))
Killillion	10^{3*10^3,000+3}	f₂(f₂(9955))
Vecekillillion	10^{3*10^30,000+3}	f₂(f₂(f₂(13)))
Googolplexigong	10^{10^100,000}	f₂(f₂(f₂(14)))
Hectekillillion	10^{3*10^300,000+3}	f₂(f₂(f₂(16)))

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Class 4 ($10^{10^{1,000,000}}$ - $10^{10^{10^{10^{1,000,000}}}}$)

Name	Value	Approximation (fast-growing hierarchy)
Millionduplex	10^{10^1,000,000}	f₂³(17)
Megillion	10^{3*10^3,000,000+3}	f₂³(21)
Gigillion	10^{3*10^{3,000,000,000}+3}	f₂³(32)
Tetralogue	10^{10^10¹⁰}	f₂³(35)
Terillion	10^{310^310¹²+3}	f₂³(37)
Petillion	10^{310^310¹⁵+3}	f₂³(47)
Exillion	10^{310^310¹⁸+3}	f₂³(57)
Zettillion	10^{310^310²¹+3}	f₂³(67)
Yottillion	10^{310^310²⁴+3}	f₂³(76)
Xennillion	10^{310^310²⁷+3}	f₂³(86)
Dakillion	10^{310^310³⁰+3}	f₂³(96)
Hendillion	10^{310^310³³+3}	f₂³(106)
First Skewes' number	e^{e^e⁷⁹} ~ 10^{10^10³⁴}	f₂³(108)
Dokillion	10^{310^310³⁶+3}	f₂³(116)
Tradakillion	10^{310^310³⁹+3}	f₂³(126)
Tedakillion	10^{310^310⁴²+3}	f₂³(134)
Ikillion	10^{310^310⁶⁰+3}	f₂³(195)
Trakillion	10^{310^310⁹⁰+3}	f₂³(294)
Googolduplex	10^{10^10¹⁰⁰}	f₂³(324)
Fzgoogolplex	(10^10¹⁰⁰)^{10^10¹⁰⁰} = 10^{10^{10¹⁰⁰+100}}	f₂³(326)
Tekillion	10^{310^310¹²⁰+3}	f₂³(393)
Hotillion	10^{310^310³⁰⁰+3}	f₂³(990)
Ecetonduplex	10^{10^10³⁰³}	f₂³(998)
Megafaxul	((200!)!)! ~ 10^{10^10³⁷⁹}	f₂³(1235)
Botillion	10^{310^{310⁶⁰⁰}+3}	f₂³(1986)
Trotillion	10^{310^{310⁹⁰⁰}+3}	f₂³(2982)
Second Skewes number	e^{e^{e^{e^7.705}}} ~ 10^{10^10⁹⁶³}	f₂³(3189)
Totillion	10^{310^{310^1,200}+3}	f₂³(3978)
Kalillion	10^{310^{310^3,000}+3}	f₂³(9956)
Dalillion	10^{310^{310^6,000}+3}	f₂³(19921)
Tralillion	10^{310^{310^9,000}+3}	f₂³(29886)
Talillion	10^{310^{310^12,000}+3}	f₂³(39851)
Dakalillion	10^{310^{310^30,000}+3}	f₂³(99645)
Googolduplexigong	10^{10^{10^100,000}}	f₂⁴(14)
Hotalillion	10^{310^{310^300,000}+3}	f₂⁴(16)

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Class 5 ($10^{10^{10^{10^6}}}$ - $10^{10^{10^{10^{10^6}}}}$)

Name	Value	Approximation (fast-growing hierarchy)
Millitriplexion	10^{10^{10^1,000,000}}	f₂⁴(16)
Mejillion	10^{310^{310^3,000,000}+3}	f₂⁴(19)
Gijillion	10^{310^{310^300,000,0000}+3}	f₂⁴(28)
Pentalogue	10^{10^{10^10¹⁰}}	f₂⁴(30)
Astillion	10^{310^{310^3*10¹²}+3}	f₂⁴(38)
Lunillion	10^{310^{310^3*10¹⁵}+3}	f₂⁴(47)
Fermillion	10^{310^{310^3*10¹⁸}+3}	f₂⁴(57)
Glocillion	10^{310^{310^3*10³⁰}+3}	f₂⁴(96)
Multillion	10^{310^{310^3*10⁴²}+3}	f₂⁴(136)
Metillion	10^{310^{310^3*10⁴⁵}+3}	f₂⁴(146)
Googoltriplex	10^{10^{10^10¹⁰⁰}}	f₂⁴(326)
Fzgargoogolplex	googolduplex^googolduplex	f₂⁴(326)
Ecetontriplex	10^{10^{10^10³⁰³}}	f₂⁴(998)
Gigafaxul	(((200!)!)!)! ~ 10^{10^{10^10³⁷⁹}}	f₂⁴(1242)
Googoltriplexigong	10^{10^{10^{10^100,000}}}	f₂⁵(14)

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Tetration level ($10^{10^{10^{10^{10^6}}}}$ - $10 \uparrow\uparrow\uparrow 3$)

Name	Value
Hexalogue	10↑↑6
Googolquadruplex	E100#5
Fzgargantugoogolplex	googoltriplex^{googoltriplex}
Heptalogue	10↑↑7
Googolquinplex	E100#6
Octalogue	10↑↑8
Googolsextiplex	E100#7
Ennalogue	10↑↑9
Bentley's Number	$\sum^{9}_{i = 0} 10 \uparrow\uparrow i$
Googolseptiplex	E100#8
Decker	{10,10,2} = 10↑↑10
Googoloctiplex	E100#9
Endekalogue / Equinoxal	10↑↑11 = 10^(≡) = 10⁽¹⁰⁾₍₁₀₎
Googolnoniplex	E100#10
Dodekalogue	10↑↑12
Googoldeciplex	E100#11
Triadekalogue	10↑↑13
Tetradekalogue	10↑↑14
Giggol	{10,100,2} = 10↑↑100
Grangol	E100#100
Expofaxul	200!1
Mega	2[5] = 256[4] ~ 10↑↑258
Chilialogue	10↑↑1,000
Myrialogue	10↑↑10,000
Grangolgong	E100,000#100,000
Tritri	{3,3,3} = {3,7625597484987,2} = 3↑↑7,625,597,484,987
Googol-stack	10↑↑(10¹⁰⁰)
Googoldex	E100#(10¹⁰⁰) = E100#1#2
Jaghanya Parīta Asaṃkhyāta	~ 10↑↑10¹³⁶
Ecetondex	E303#1#2
Grand Faxul	~ 10↑↑10³⁷⁹
Zootzootplex	Exponential factorial of googolplex = googolplex^{googolplex-1^{googolplex-2^{...^{4^3²}}}}.
Googolplexstack	10↑↑(10^10¹⁰⁰)
Googolplexidex	E100#(10^10¹⁰⁰) = E100#2#2
Grand Kilofaxul	~ 10↑↑10^10³⁷⁹

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Up-arrow notation level ($10 \uparrow\uparrow\uparrow 3$ - $f_\omega(f_3(10))$)

Name	Value
Tria-taxis	E1#1#3 = 10↑↑↑3 = 10↑↑10↑↑10
Equiduoxal	10^(≡≡) = 10^{(10^(≡))}_(10^(≡))
Giggolplex	{10,giggol,2} = 10↑↑10↑↑100
Grangoldex	E100#100#2
Kiloexpofaxul	(200!1)!1
Grangoldexigong	E100,000#100,000#2
Googolgoogolduplex	10↑↑10↑↑(10¹⁰⁰)
Ecetondudex	E303#1#3
Bigrand Faxul	~ 10↑↑10↑↑(10³⁷⁹)
Tetra-taxis	E1#1#4 = 10↑↑↑4
Giggolduplex	{10,giggolplex,2} = 10↑↑10↑↑10↑↑100
Grangoldudex	E100#100#3
Megaexpofaxul	((200!1)!1)!1
Grangoldudexigong	E100,000#100,000#3
Googolgoogoltriplex	10↑↑10↑↑10↑↑(10¹⁰⁰)
Grangoltridex	E100#100#4
{{fancyK}} (fancy K)	10↑↑↑10
Megiston	10[5] ~ 10↑↑↑11
Gaggol	{10,100,3} = 10↑↑↑100
Greagol	E100#100#100
Tetrofaxul	200!2
Greagolgong	E100,000#100,000#100,000
Googol-3-flex	10↑↑↑(10¹⁰⁰)
Ecetonthrex	E303#1#1#2
Folkman's number	2↑↑↑(2⁹⁰¹)
Grand expofaxul	~ 10↑↑↑10↑↑198
A-ooga	2[6]
Grahal	g₁ = 3↑↑↑↑3
Super K	10↑↑↑↑3
Gaggolplex	{10,gaggol,3}
Greagolthrex	E100#100#100#2
Kilotetrofaxul	(200!2)!2
Greagolthrexigong	E100,000#100,000#100,000#2
Ecetonduthrex	E303#1#1#3
Tritet	{4,4,4} = 4↑↑↑↑4
Greagolduthrex	E100#100#100#3
Greagolduthrexigong	E100,000#100,000#100,000#3
Equitrioxal	10^(≡≡≡) = 10^{(10^(≡≡))}_{(10^(≡≡))}
Hexar	$Q_{1,0}(6)$ = 6↑↑↑↑6
Deka-petaxis	{10,10,4} = 10↑↑↑↑10
Geegol	{10,100,4} = 10↑↑↑↑100
Gigangol	E100#100#100#100
Pentofaxul	200!3
Geegolplex	{10,geegol,4}
Gigangoltetrex	E100#100#100#100#2
Gigangoldutetrex	E100#100#100#100#3
Tripent	{5,5,5} = 5↑↑↑↑↑5
Deka-exaxis	10↑↑↑↑↑10
Gigol	{10,100,5} = 10↑↑↑↑↑100
Gorgegol	E100#100#100#100#100
Hexofaxul	200!4
Gigolplex	{10,gigol,5}
Gorgegolpentex	E100#100#100#100#100#2
Goggol	{10,100,6}= 10↑↑↑↑↑↑100
Gulgol	E100#100#100#100#100#100
Goggolplex	{10,goggol,6}
Gulgolhex	E100#100#100#100#100#100#2
Trisept	{7,7,7} = 7↑⁷7
Gagol	{10,100,7} = 10↑⁷100
Gaspgol	E100#100#100#100#100#100#100
Gagolplex	{10,gagol,7}
Gaspgolheptex	E100#100#100#100#100#100#100#2
Ginorgol	E100#100#100#100#100#100#100#100
Ginorgoloctex	E100#100#100#100#100#100#100#100#2
Gargantuul	E100##9
Tridecal	{10,10,10}
Googondol	E100##10
Boogol	{10,10,100}
Gugold	E100##100
Hyperfaxul	200![1]
Gugoldagong	E100,000##100,000
Gongol	hyper(10,10¹⁰⁰,100)
Googoldiflux	10↑^{10^100}10^100
Equiquinoxal	10^{(≡{≡}≡)}
$q(6)$ (lower bound)

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Linear omega level ($f_\omega(f_3(10))$ - $f_{\omega^2}(f_3(10))$)

Name	Value
Moser	2[2[5]] using Steinhaus-Moser notation, ~ 3 ↑^Mega 3
Boogolplex	{10,10,{10,10,100}}
Gugolda-suplex	E100##100#2
Kilohyperfaxul	(200![1])![1]
Gongolplex	hyper(10,gongol,100)
Dihexar	$Q_{1,1}(6) \approx 6\rightarrow 6\rightarrow 6\rightarrow 2$
Little Graham
Graham's number	g₆₄, where g₁ = 3 ↑⁴ 3 and g_n = 3 ↑^g_n-1 3, ~ {3,65,1,2}
xkcd number	A(G,G), where G is Graham's number, ~ {3,66,1,2}
Corporal	{10,100,1,2}
Graatagold	E100##100#100
Forcal	g_1,000,000
Conway's Tetratri	3→3→3→3 ~ {3³,3,2,2}
Corporalplex	{10,{10,100,1,2},1,2}
Graatagolda-sudex	E100##100#100#2
Force forcal	g_forcal
Trihexar	$Q_{1,2}(6)$
Greegold	E100##100#100#100
Suporcal	Forcal(1,000,000)
Greegolda-suthrex	E100##100#100#100#2
Grinningold	E100##100#100#100#100
Megocal	Forcal₂(1,000,000)
Golaagold	E100##100##5
Gruelohgold	E100##100##6
Gaspgold	E100##100##7
Ginorgold	E100##100##8
Grand tridecal	{10,10,10,2}
Gugolthra	E100##100##100
Biggol	{10,10,100,2}
Giaxul	200![200] = 200![1,2]
Ultron	$\approx f_{\omega+200} (100)$
Terribocal	Forcal_1,2(1)
Biggolplex	{10,10,{10,10,100,2},2}
Graatagolthra	E100##100##100#100
Greegolthra	E100##100##100#100#100
Tetratri	{3,3,3,3}
Septasexahexar	$Q_{3,0}(6)$
Gugoltesla	E100##100##100##100
Baggol	{10,10,100,3}
Tribocal	Forcal_1,3(1)
Baggolplex	{10,10,{10,10,100,3},3}
Graatagoltesla	E100##100##100##100#100
Supertet	{4,4,4,4}
Gugolpeta	E100##100##100##100##100
Beegol	{10,10,100,4}
Beegolplex	{10,10,{10,10,100,4},4}
Gugolhexa	E100###6
Bigol	{10,10,100,5}
Gugolhepta	E100###7
Boggol	{10,10,100,6}
Gugolocta	E100###8
Bagol	{10,10,100,7}
General	{10,10,10,10}
Kaboodol	$\underbrace{10 \rightarrow\ldots\rightarrow 10}_{102} < \text{kaboodol} < \underbrace{10 \rightarrow\ldots\rightarrow 10}_{103}$
Throogol	E100###100
Troogol	{10,10,10,100}
Giabixul	200![200,200]

More...

Quadratic omega level ($f_{\omega^2}(f_3(10))$ - $f_{\omega^3}(f_3(10))$)

Name	Value
Generalplex	{10,10,10,{10,10,10,10}} = {10,3,1,1,2}
Kaboodolplex	$\underbrace{10 \rightarrow\ldots\rightarrow 10}_{\text{kaboodol}+2} < \text{kaboodolplex} < \underbrace{10 \rightarrow\ldots\rightarrow 10}_{\text{kaboodol}+3}$
Troogolplex	{10,10,10,{10,10,10,100}}
Thrangol	E100###100#100
BOX_M̃
Threagol	E100###100#100#100
Thrugold	E100###100##100
Thrugolthra	E100###100##100##100
Thrugoltesla	E100###100##100##100##100
Throotrigol	E100###100###100
Triggol	{10,10,10,100,2}
Triggolplex	{10,10,10,{10,10,10,100,2},2}
Thrantrigol	E100###100###100#100
Thrutrigold	E100###100###100##100
Pentatri	{3,3,3,3,3}
Throotergol	E100###100###100###100
Traggol	{10,10,10,100,3}
Throopetol	E100###100###100###100###100
Treegol	{10,10,10,100,4}
Superpent	{5,5,5,5,5}
Throohexol	E100####6
Trigol	{10,10,10,100,5}
Throoheptgol	E100####7
Troggol	{10,10,10,100,6}
Throogogdol	E100####8
Tragol	{10,10,10,100,7}
Pentadecal	{10,10,10,10,10}
Tetroogol	E100####100
Quadroogol	{10,10,10,10,100}

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Polynomial omega level ($f_{\omega^3}(f_3(10))$ - $f_{\omega^\omega}(f_3(10))$)

Name	Value
Pentadecalplex	{10,10,10,10,{10,10,10,10,10}}
Quadroogolplex	{10,10,10,10,{10,10,10,10,100}}
Tetrangol	E100####100#100
Tetrugold	E100####100##100
Tetrithroogol	E100####100###100
Tetrootrigol	E100####100####100
Quadriggol	{10,10,10,10,100,2}
Hexatri	{3,3,3,3,3,3}
Tetrootergol	E100####100####100####100
Quadraggol	{10,10,10,10,100,3}
Tetroopetol	E100####100####100####100####100
Quadreegol	{10,10,10,10,100,4}
Tetroohexol	E100#####6
Quadrigol	{10,10,10,10,100,5}
Superhex	{6,6,6,6,6,6}
Tetrooheptgol	E100#####7
Quadroggol	{10,10,10,10,100,6}
Tetroogogdol	E100#####8
Quadragol	{10,10,10,10,100,7}
Hexadecal	{10,10,10,10,10,10}
Pentoogol	E100#####100
Quintoogol	{10,10,10,10,10,100}
Pentootrigol	E100#####100#####100
Quintiggol	{10,10,10,10,10,100,2}
Pentootergol	E100#####100#####100#####100
Quintaggol	{10,10,10,10,10,100,3}
Quinteegol	{10,10,10,10,10,100,4}
Quintigol	{10,10,10,10,10,100,5}
Supersept	{7,7,7,7,7,7,7}
Heptadecal	{10,10,10,10,10,10,10}
Hexoogol	E100######100
Sextoogol	{10,10,10,10,10,10,100}
Superoct	{8,8,8,8,8,8,8,8}
Octadecal	{10,10,10,10,10,10,10,10}
Heptoogol	E100#######100
Septoogol	{10,10,10,10,10,10,10,100}
Superenn	{9,9,9,9,9,9,9,9,9}
Ennadecal	{10,10,10,10,10,10,10,10,10}
Ogdoogol	E100########100
Octoogol	{10,10,10,10,10,10,10,10,100}
Iteral	{10,10,10,10,10,10,10,10,10,10} = {10,10 (1) 2} = {10,2,2 (1) 2}
Entoogol	E100#########100
Dektoogol	E100##########100
Ultatri	{3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3} = {3,27 (1) 2}
Goobol	{10,100(1)2}
Godgahlah	E100#¹⁰⁰100 = E100#^#100
Giatrixul	200![200,200,200]
Godgahlahgong	E100,000#^100,000100,000

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Exponentiated linear omega level ($f_{\omega^\omega}(f_3(10))$ - $f_{\omega^{\omega^2}}(f_3(10))$)

Name	Value
Dupertri	{3,{3,3,3}(1)2} = {3,3,2 (1) 2}
Duperdecal	{10,{10,10(1)2}(1)2}
Goobolplex	{10,{10,100(1)2}(1)2}
Grand godgahlah	E100#^godgahlah100 = E100#^#100#2
Grand godgahlahgong	E100,000#^{godgahlahgong}100,000
Grand grand godgahlah	E100#^#100#3
Gibbol	{10,100,2(1)2}
Grandgahlah	E100#^#100#100
Latri	{3,3,3(1)2}
Gabbol	{10,100,3(1)2}
Greagahlah	E100#^#100#100#100
Boobol	{10,10,100(1)2}
Gugoldgahlah	E100#^#100##100
Bibbol	{10,10,100,2(1)2}
Gugolthragahlah	E100#^#100##100##100
Troobol	{10,10,10,100(1)2}
Throogahlah	E100#^#100###100
Quadroobol	{10,10,10,10,100(1)2}
Tetroogahlah	E100#^#100####100
Gootrol	{10,100(1)3}
Gotrigahlah	E100#^#100#^#100
Bootrol	{10,10,100(1)3}
Gooquadrol	{10,100(1)4}
Gotergahlah	E100#^#100#^#100#^#100
Emperal	{10,10(1)10}
Gossol	{10,10(1)100}
Godgoldgahlah	E100#^#*#100
Emperalplex	{10,10(1){10,10(1)10}}
Gossolplex	{10,10(1){10,10(1)100}}
Gotrigoldgahlah	E100#^##100#^##100
Gissol	{10,10(1)100,2}
Gassol	{10,10(1)100,3}
Hyperal	{10,10(1)10,10}
Fish number 3	$F_3^{63}(3)$
Mossol	{10,10(1)10,100}
Godthroogahlah	E100#^#*##100
Mossolplex	{10,10(1)10,{10,10(1)10,100}}
Bossol	{10,10(1)10,10,100}
Godtetroogahlah	E100#^#*###100
Trossol	{10,10(1)10,10,10,100}
Godpentoogahlah	E100#^#*####100
Quadrossol	{10,10(1)10,10,10,10,100}
Quintossol	{10,10(1)10,10,10,10,10,100}
Diteral	{10,10 (1)(1) 2}
Dubol	{10,100 (1)(1) 2}
Deutero-godgahlah	E100#^#*#^#100
Diteralplex	{10,diteral (1)(1) 2}
Dutrol	{10,100 (1)(1) 3}
Duquadrol	{10,100 (1)(1) 4}
Admiral	{10,10 (1)(1) 10}
Dossol	{10,10 (1)(1) 100}
Deutero-godgoldgahlah	E100#^##^##100
Dossolplex	{10,10 (1)(1) dossol}
Dutritri	{3,3,3 (1) 3,3,3 (1) 3,3,3}
Dutridecal	{10,10,10 (1) 10,10,10 (1) 10,10,10}
Trito-godgahlah	E100#^##^##^#100
Teterto-godgahlah	E100#^##^##^#*#^#100
Pepto-godgahlah	E100#^##5
Exto-godgahlah	E100#^##6
Epto-godgahlah	E100#^##7
Ogdo-godgahlah	E100#^##8
Xappol	{10,10 (2) 2}
Goxxol	{10,100 (2) 2}
Gridgahlah	E100#^##100

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Exponentiated polynomial omega level ($f_{\omega^{\omega^2}}(f_3(10))$ - $f_{\omega^{\omega^\omega}}(f_3(10))$)

Name	Number
Xappolplex	{10,xappol (2) 2}
Grand gridgahlah	E100#^##100#2
Grand xappol	{10,10 (2) 3}
Gridtrigahlah	E100#^##100#^##100
Deutero-gridgahlah	E100#^##*#^##100
Dimentri	{3,3 (3) 2}
Trito-gridgahlah	E100#^###^###^##100
Teterto-gridgahlah	E100#^###^###^##*#^##100
Colossol	{10,10 (3) 2}
Kubikahlah	E100#^###100
Colossolplex	{10,colossol (3) 2}
Deutero-kubikahlah	E100#^###*#^###100
Trito-kubikahlah	E100#^####^####^###100
Terossol	{10,10 (4) 2}
Quarticahlah	E100#^####100
Terossolplex	{10,terossol (4) 2}
Deutero-quarticahlah	E100#^####*#^####100
Petossol	{10,10 (5) 2}
Quinticahlah	E100#^#####100
Petossolplex	{10,petossol (5) 2}
Ectossol	{10,10 (6) 2}
Sexticahlah	E100#^######100
Ectossolplex	{10,ectossol (6) 2}
Zettossol	{10,10 (7) 2}
Septicahlah	E100#^#######100
Zettossolplex	{10,zettossol (7) 2}
Yottossol	{10,10 (8) 2}
Octicahlah	E100#^########100
Yottossolplex	{10,yottossol (8) 2}
Nonicahlah	E100#^#^#9
Xennossol	{10,10 (9) 2}
Xennossolplex	{10,xennossol (9) 2}
Dimendecal	{10,10 (10) 2}
Decicahlah	E100#^#^#10
Gongulus	{10,10 (100) 2}
Godgathor	E100#^#^#100

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Double exponentiated polynomial omega level ($f_{\omega^{\omega^\omega}}(f_3(10))$ - $f_{\omega^{\omega^{\omega^\omega}}}(f_3(10))$)

Name	Value
Gongulusplex	{10,10 (gongulus) 2}
Grand godgathor	E100#^#^#100#2
Gongulusduplex	{10,10 (gongulusplex) 2}
Gotrigathor	E100#^#^#100#^#^#100
Deutero-godgathor	E100#^#^#*#^#^#100
Trito-godgathor	E100#^#^##^#^##^#^#100
Hecato-godgathor	E100#^(#^#*#)100
Godgridgathor	E100#^(#^#*##)100
Dulatri	{3,3 (0,2) 2}
Godkubikgathor	E100#^(#^#*###)100
Gingulus	{10,100 (0,2) 2}
Godgathordeus	E100#^(#^#*#^#)100
Trilatri	{3,3 (0,3) 2}
Gangulus	{10,100 (0,3) 2}
Godgathortruce	E100#^(#^##^##^#)100
Geengulus	{10,100 (0,4) 2}
Godgathorquad	E100#^(#^##^##^#*#^#)100
Gowngulus	{10,100 (0,5) 2}
Godgathorquid	E100#^#^##5
Gungulus	{10,100 (0,6) 2}
Godgathorsid	E100#^#^##6
Bongulus	{10,100 (0,0,1) 2}
Gralgathor	E100#^#^##100
Bingulus	{10,100 (0,0,2) 2}
Gralgathordeus	E100#^(#^##*#^##)100
Trimentri	{3,3 (0,0,0,1) 2} = {3,3 ((1)1) 2}
Bangulus	{10,100 (0,0,3) 2}
Gralgathortruce	E100#^(#^###^###^##)100
Beengulus	{10,100 (0,0,4) 2}
Trongulus	{10,100 (0,0,0,1) 2}
Thraelgathor	E100#^#^###100
Thraelgathordeus	E100#^(#^###*#^###)100
Quadrongulus	{10,100 (0,0,0,0,1) 2}
Terinngathor	E100#^#^####100
Pentaelgathor	E100#^#^#####100
Hexaelgathor	E100#^#^######100
Heptaelgathor	E100#^#^#######100
Octaelgathor	E100#^#^########100
Goplexulus	$\lbrace10,100 (\underbrace{0,0,\ldots ,0,0,}_{100 \text{ zeroes}}1) 2\rbrace$ = {10,100 ((1)1) 2}
Godtothol	E100#^#^#^#100

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Triple exponentiated polynomial omega level ($f_{\omega^{\omega^{\omega^\omega}}}(f_3(10))$ - $f_{\omega^{\omega^{\omega^{\omega^\omega}}}}(f_3(10))$)

Name	Value
Godtotholdeus	E100#^(#^#^#*#^#^#)100
Godtotholcentice	E100#^#^(#^#*#)100
Hyper-godgathordeuterfact	E100#^#^(#^#*##)100
Hyper-godgathordeus	E100#^#^(#^#*#^#)100
Extendol	s(3,3{1`2}2)
Hyper-godgathortruce	E100#^#^(#^##^##^#)100
Graltothol	E100#^#^#^##100
Hyper-gralgathordeus	E100#^#^(#^##*#^##)100
Thraeltothol	E100#^#^#^###100
Terinntothol	E100#^#^#^####100
Pentaeltothol	E100#^#^#^#####100
Goduplexulus	{10,100 ((100)1) 2} = {10,100 ((0,1)1) 2}
Godtertol	E100#^#^#^#^#100

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Iterated Cantor normal form level ($f_{\omega^{\omega^{\omega^{\omega^\omega}}}}(f_3(10))$ - $f_{\varepsilon_0}^2(10)$)

Name	Value
Hyper-hyper-godgathordeus	E100#^#^#^(#^#*#^#)100
Graltertol	E100#^#^#^#^##100
Thraeltertol	E100#^#^#^#^###100
Gotriplexulus	$\lbrace 10,100 ((\underbrace{0,0,\ldots ,0,0,}_{100 \text{ zeroes}}1)1) 2\rbrace$ = {10,100 (((1)1)1) 2}
Godtopol	E100#^#^#^#^#^#100
Graltopol	E100#^#^#^#^#^##100
Godhathor	E100#^#^#^#^#^#^#100
Godheptol	E100#^#^#^#^#^#^#^#100
Godoctol	E100#^#^#^#^#^#^#^#^#100
Godentol	E100#^#^#^#^#^#^#^#^#^#100
Goddekathol	E100#^#^#^#^#^#^#^#^#^#^#100
Tethrathoth	E100#^^#100
Goppatoth	10↑↑100 & 10
Nucleaxul	200![₂₀₀200]
Giaquaxul	200![200,200,200,200]

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Epsilon level ($f_{\varphi(1,0)}^2(10)$ aka $f_{\varepsilon_0}^2(10)$ - $f_{\varphi(2,0)}^2(10)$ aka $f_{\zeta_0}^2(10)$)

Name	Value
Grand tethrathoth	E100#^^#100#2
Goppatothplex	10↑↑(goppatoth) & 10
Grantethrathoth	E100#^^#100#100
Gugolda-carta-tethrathoth	E100#^^#100##100
Godgahlah-carta-tethrathoth	E100#^^#100#^#100
Tethratrithoth	E100#^^#100#^^#100
Tethraterthoth	E100#^^#100#^^#100#^^#100
Tethrathoth-by-hyperion	E100#^^#*#100
Tethrathoth-by-godgahlah	E100#^^#*#^#100
Tethrathoth-by-godgathor	E100#^^#*#^#^#100
Deutero-tethrathoth	E100#^^#*#^^#100
Trito-tethrathoth	E100#^^##^^##^^#100
Hecato-tethrathoth	E100(#^^#)^#100
Grideutertethrathoth	E100(#^^#)^##100
Tethragodgathor	E100(#^^#)^#^#100
Tethraduliath	E100(#^^#)^(#^^#)100
Tethrathruliath	E100(#^^#)^(#^^#*#^^#)100
Monster-Giant	E100(#^^#)^(#^^#)^#100
Monster-Grid	E100(#^^#)^(#^^#)^##100
Monster-Hecateract	E100(#^^#)^(#^^#)^#^#100
Super Monster-Giant	E100(#^^#)^(#^^#)^(#^^#)^#100
Terrible tethrathoth	E100(#^^#)^^#100
Terrible terrible tethrathoth	E100((#^^#)^^#)^^#100
Tethrathoth ba'al	E100#^^#>#100
Great and Terrible Tethrathoth	E100#^^#>#100#2
Grangol-carta-tethriterator	E100#^^#>#100#100
Tethriterhecate	E100#^^#>#*#100
Deutero-tethriterator	E100#^^#>#*#^^#>#100
Tethriterfact	E100(#^^#>#)^#100
Terrible tethriterator	E100(#^^#>#)^^#100
Tethriditerator	E100#^^#>(#+#)100
Tethrigriditerator	E100#^^#>##100
Tethrispatialator	E100#^^#>#^#100
Dustaculated-tethrathoth	E100#^^#>#^^#100
Gippatoth	100↑↑(2 × 100) & 10
Tristaculated-tethrathoth	E100#^^#>#^^#>#^^#100
Gappatoth	100↑↑(3 × 100) & 10
Geepatoth	100↑↑(4 × 100) & 10
Tethracross	E100#^^##100
Boppatoth	100↑↑(100²) & 10

More...

Binary phi level ($f_{\varphi(2,0)}^2(10)$ or $f_{\zeta_0}^2(10)$ - $f_{\varphi(1,0,0)}^2(10)$ or $f_{\Gamma_0}^2(10)$)

Name	Value
Terrible tethracross	E100(#^^##)^^#100
Tethriterated-tethracross	E100(#^^##)^^#>#100
Secundotethrated-tethracross	E100(#^^##)^^##100
Tethritercross	E100#^^##>#100
Dustaculated-tethracross	E100#^^##>#^^##100
Tethracubor	E100#^^###100
Troppatoth	100↑↑(100³) & 10
Terrible tethracubor	E100(#^^###)^^#100
Terrisquared-tethracubor	E100(#^^###)^^##100
Tethraducubor	E100(#^^###)^^###100
Tethritercubor	E100#^^###>#100
Dustaculated-tethracubor	E100#^^###>#^^###100
Tethrateron	E100#^^####100
Quadroppatoth	100↑↑(100⁴) & 10
Terrible tethrateron	E100(#^^####)^^#100
Tethraduteron	E100(#^^####)^^####100
Tethra-hectateron	E100#^^####>#100
Dustaculated-tethrateron	E100#^^####>#^^####100
Tethrapeton	E100#^^#####100
Tethrahexon	E100#^^######100
Tethrahepton	E100#^^#^#7
Tethra-ogdon	E100#^^#^#8
Tethrennon	E100#^^#^#9
Tethradekon	E100#^^#^#10
Tethratope	E100#^^#^#100
Tethratopothoth	E100#^^(#^#*#)100
Tethratopodeus	E100#^^(#^#*#^#)100
Tethralattitope	E100#^^#^##100
Tethrato-godgathor	E100#^^#^#^#100
Tethrato-godtothol	E100#^^#^#^#^#100
Tethrato-tethrathoth	E100#^^#^^#100
Tethrarxitet	E100#^^#^^#^^#100
Pentacthulhum	E100#^^^#100
Kungulus	X↑↑↑100 & 10

More...

Bachmann's collapsing level ($f_{\varphi(1,0,0)}^2(10)$ or $f_{\Gamma_0}^2(10)$ - $f_{\psi_0(\varepsilon_{\Omega+1})}^2(10) = f_{\psi_0(\Omega_2)}^2(10)$ with respect to the Buchholz's function)

Name	Value
Pentacthuldugon	E100(#^^^#)^^^#100
Pentacthuliterator	E100#^^^#>#100
Hugexul	200![200(1)200]
Superior Hugexul	200![200(1)200,200]
Dustaculated-pentacthulhum	E100#^^^#>#^^^#100
Pentacthulcross	E100#^^^##100
Bisuperior Hugexul	200![200(1)200,200,200]
Pentacthulcubor	E100#^^^###100
Pentacthulteron	E100#^^^####100
Pentacthultope	E100#^^^#^#100
Pentacthularxitri	E100#^^^#^^^#100
Hexacthulhum	E100#^^^^#100
Hugebixul	200![200(1)200(1)200]
Hexacthuliterator	E100#^^^^#>#100
Superior Hugebixul	200![200(1)200(1)200,200]
Hexacthulcross	E100#^^^^##100
Hexacthultope	E100#^^^^#^#100
Heptacthulhum	E100#^^^^^#100 = E100#{5}#100
Hugetrixul	200![200(1)200(1)200(1)200]
Ogdacthulhum	E100#^^^^^^#100 = E100#{6}#100
Hugequaxul	200![200(1)200(1)200(1)200(1)200]
Ennacthulhum	E100#{7}#100
Dekacthulhum	E100#{8}#100
Goliath	E100#{10}#100
Godsgodgulus	E100#{#}#100
Godsgodeugulus	E100(#{#}#){#}#100
Godsgodguliterator	E100#{#}#>#100
Godsgodgulcross	E100#{#}##100
Godsgodgultope	E100#{#}#^#100
Godsgodarxitri	E100#{#}#{#}#100
Godsgodeus	E100#{#+#}#100
The centurion	E100#{#^#}#100
Super centurion	E100#{#^^#}#100
Ohmygosh-ohmygosh-ohmygooosh	E100#{#{#}#}#100
Blasphemorgulus	E100{#,#,1,2}100
Hundrelasphemorgue	E100{#,#+1,1,2}100
Enormaxul	200![200(2)200]
Superior Enormaxul	200![200(2)200,200]
Bisuperior Enormaxul	200![200(2)200,200,200]
Enormabixul	200![200(2)200(2)200]
Enormatrixul	200![200(2)200(2)200(2)200]
Enormaquaxul	200![200(2)200(2)200(2)200(2)200]
Goobawamba	{10,100 (1) 2} & 10
Destruxul	200![200(200)200]
Great Destruxul	200![200(200)200(200)200]
Bigreat Destruxul	200![200(200)200(200)200(200)200]
Bird's number	$f_{\vartheta(\Omega^{\omega})+2}(f_{\vartheta(\Omega^{\omega})+1}(f_{\vartheta(\Omega^{\omega})}(f_{\vartheta(\Omega^{\omega})}(7))))$
TREE(3) (lower bound)
Destrubixul	200![200([200(200)200])200]
Destrutrixul	200![200([200([200(200)200])200])200]
Destruquaxul	200![200([200([200([200(200)200])200])200])200]
Golapulus	10¹⁰⁰&10&10
Ginglapulus	{10,100 (0,2) 2} & 10
Ganglapulus	{10,100 (0,3) 2} & 10
Geenglapulus	{10,100 (0,4) 2} & 10
Bolapulus	{10,100 (0,0,1) 2} & 10
Binglapulus	{10,100 (0,0,2) 2} & 10
Trolapulus	{10,100 (0,0,0,1) 2} & 10
Quadrolapulus	{10,100 (0,0,0,0,1) 2} & 10
Goplapulus	{10,100 ((1)1) 2} & 10
Giplapulus	{10,100 ((1)(1)1) 2} & 10
Boplapulus	{10,100 ((2)1) 2} & 10
Goduplapulus	{10,100 ((0,1)1) 2} & 10
Gotriplapulus	{10,100 (((1)1)1) 2} & 10
Extremexul	200![1(1)[₂200,200,200,200]]

More...

Higher computable level ($f_{\psi_0(\varepsilon_{\Omega+1})}^2(10) = f_{\psi_0(\psi_2(0))}^2(10)$ with respect to Buchholz's function - ???)

Since the comparison (or even the well-definedness) of numbers of this level is unknown, the order of entries does not necessarily imply the order of the sizes. Also, several numbers are defined by an OCF, which is uncomputable, and are not known to be computable.

Name	Value
Extremebixul	200![1(1)[₂200,200,200,200,200]]
Extremetrixul	200![1(1)[₂200,200,200,200,200,200]]
Extremequaxul	200![1(1)[₂200,200,200,200,200,200,200]]
Gigantixul	200![1(1)[₃200,200,200]]
Gigantibixul	200![1(1)[₃200,200,200,200]]
Gigantitrixul	200!1(1)[₃200,200,200,200,200]]
Gigantiquaxul	200![1(1)[₃200,200,200,200,200,200]]
Nucleabixul	200![_{[₂₀₀200]}200]
SCG(13) (lower bound)
段階配列数	g¹⁰⁰(100)
Nucleatrixul	200![_{[_{[₂₀₀200]}200]}200]
Nucleaquaxul	200![_{[_{[_{[₂₀₀200]}200]}200]}200]
Kumakuma 3 variables ψ number	F^10¹⁰⁰(^10¹⁰⁰)
グラハム数ver ε.0.1.0	G⁶⁴(4)
Loader's number	D⁵(99)
Bashicu matrix number with respect to Bashicu matrix system version 2.3
６ (N primitive)
Y sequence number	f²⁰⁰⁰(1)
the least transcendental integer

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Uncomputable numbers

The term "uncomputable number" here refers to the numbers defined in terms of uncomputably fast-growing functions. This table contains large numbers which are known to be ill-defined. For more details on the ill-definedness, click the "More..." link below.

Name	Value	Ill-defined?
1919-th busy beaver	$\Sigma(1919)$	No
Fish number 4	F₄⁶³(3)	No
$\Xi(10^6)$		No
$\Sigma_\infty(10^9)$		No
Rayo's number	Rayo(10¹⁰⁰)	Partially (see #Axiom)
Fish number 7	F₇⁶³(10¹⁰⁰)	Partially
BIG FOOT	FOOT¹⁰(10¹⁰⁰)	Yes (see #Ill-definedness)
Little Bigeddon		Yes
Sasquatch		Yes
Large Number Garden Number	$f^{10}(10 \uparrow^{10} 10)$	Not determined yet
Oblivion		Yes (unformalised)
Utter Oblivion		Yes (unformalised)

More...

Notes

^ (S) means "in the short scale", and (L) means "in the long scale".

[1] (S) means "in the short scale", and (L) means "in the long scale".

[1]

User:Numspan33/sandbox

Contents

Class 0 (0 - 6)

Class 1 (7 - 1,000,000)

Class 2 (1,000,000 - \(10^{1,000,000}\))

Class 3 (\(10^{1,000,000} - 10^{10^{1,000,000}}\))

Class 4 (\(10^{10^{1,000,000}}\) - \(10^{10^{10^{10^{1,000,000}}}}\))

Class 5 (\(10^{10^{10^{10^6}}}\) - \(10^{10^{10^{10^{10^6}}}}\))

Tetration level (\(10^{10^{10^{10^{10^6}}}}\) - \(10 \uparrow\uparrow\uparrow 3\))

Up-arrow notation level (\(10 \uparrow\uparrow\uparrow 3\) - \(f_\omega(f_3(10))\))

Linear omega level (\(f_\omega(f_3(10))\) - \(f_{\omega^2}(f_3(10))\))

Quadratic omega level (\(f_{\omega^2}(f_3(10))\) - \(f_{\omega^3}(f_3(10))\))

Polynomial omega level (\(f_{\omega^3}(f_3(10))\) - \(f_{\omega^\omega}(f_3(10))\))

Exponentiated linear omega level (\(f_{\omega^\omega}(f_3(10))\) - \(f_{\omega^{\omega^2}}(f_3(10))\))

Exponentiated polynomial omega level (\(f_{\omega^{\omega^2}}(f_3(10))\) - \(f_{\omega^{\omega^\omega}}(f_3(10))\))

Double exponentiated polynomial omega level (\(f_{\omega^{\omega^\omega}}(f_3(10))\) - \(f_{\omega^{\omega^{\omega^\omega}}}(f_3(10))\))

Triple exponentiated polynomial omega level (\(f_{\omega^{\omega^{\omega^\omega}}}(f_3(10))\) - \(f_{\omega^{\omega^{\omega^{\omega^\omega}}}}(f_3(10))\))

Iterated Cantor normal form level (\(f_{\omega^{\omega^{\omega^{\omega^\omega}}}}(f_3(10))\) - \(f_{\varepsilon_0}^2(10)\))

Epsilon level (\(f_{\varphi(1,0)}^2(10)\) aka \(f_{\varepsilon_0}^2(10)\) - \(f_{\varphi(2,0)}^2(10)\) aka \(f_{\zeta_0}^2(10)\))

Binary phi level (\(f_{\varphi(2,0)}^2(10)\) or \(f_{\zeta_0}^2(10)\) - \(f_{\varphi(1,0,0)}^2(10)\) or \(f_{\Gamma_0}^2(10)\))

Bachmann's collapsing level (\(f_{\varphi(1,0,0)}^2(10)\) or \(f_{\Gamma_0}^2(10)\) - \(f_{\psi_0(\varepsilon_{\Omega+1})}^2(10) = f_{\psi_0(\Omega_2)}^2(10)\) with respect to the Buchholz's function)

Higher computable level (\(f_{\psi_0(\varepsilon_{\Omega+1})}^2(10) = f_{\psi_0(\psi_2(0))}^2(10)\) with respect to Buchholz's function - ???)

Uncomputable numbers

Notes

Name	Value	Approximation (Fast-growing hierarchy)
Zero	0	N/A
Googolminex	\(10^{-(10^{100})}\) or 1/googolplex	N/A
Googol-minutia	\(10^{-100}\) or 1/googol	N/A
One	1	f₀(0)
Two	2	f₀(1)
Three	3	f₀(2)
Four	4	f₀(3)
Five	5	f₀(4)
Six	6	f₀(5)

Name	Value	Ill-defined?
1919-th busy beaver	\(\Sigma(1919)\)	No
Fish number 4	F₄⁶³(3)	No
\(\Xi(10^6)\)		No
\(\Sigma_\infty(10^9)\)		No
Rayo's number	Rayo(10¹⁰⁰)	Partially (see #Axiom)
Fish number 7	F₇⁶³(10¹⁰⁰)	Partially
BIG FOOT	FOOT¹⁰(10¹⁰⁰)	Yes (see #Ill-definedness)
Little Bigeddon		Yes
Sasquatch		Yes
Large Number Garden Number	\(f^{10}(10 \uparrow^{10} 10)\)	Not determined yet
Oblivion		Yes (unformalised)
Utter Oblivion		Yes (unformalised)