List of googolisms/Higher computable level

Since the comparison (or even the well-definedness) of the numbers in this level is unknown, the order of entries does not necessarily imply the order of the sizes (note that ill-defined numbers such as BEAF numbers beyond tetrational arrays, Extensible-E numbers beyond Hyper-Hyper-Extended Cascading E Notation, Hyperfactorial array notation numbers using the ? function, SAN numbers, numbers using the Dollar function, numbers defined using D Shamlin Jr's extension of Bird's array notation, and so on, should not lie in this level, see also Category:Class disputed and Talk:Meameamealokkapoowa oompa#Size issue). Also, several numbers are defined by an OCF, which is uncomputable, and are not known to be computable, particularly beyond \(\psi_0(\Phi_1(0))\) level on the fast-growing hierarchy with respect to the system of fundamental sequences for Extended Buchholz's function, where \(\psi\) is Extended Buchholz's function and \(\Phi_1(0)\) is the least omega fixed point. Moreover, several approximations are using unspecified (or even ill-defined) OCFs, and hence might be mathematically meaningless. Note that various systems of fundamental sequences are used for comparisons on this level.

\(f_{\psi_0(\Omega_2)}^2(10)\) ~ \(f_{\psi_0(\Omega_\omega)}^2(10)\)[]

Trugubrigoogol, {100,100[1[1¬4]2]2}
Omega Mega Super Even More Godder Tritri, 3 [3 {3 // 3} 3] 3
Tetrugubrigoogol, {100,100[1[1¬5]2]2}
Pentugubrigoogol, {100,100[1[1¬6]2]2}
Hexugubrigoogol, {100,100[1[1¬7]2]2}
Heptugubrigoogol, {100,100[1[1¬8]2]2}
Ogdugubrigoogol, {100,100[1[1¬9]2]2}
Ennugubrigoogol, {100,100[1[1¬10]2]2}
Dekugubrigoogol, {100,100[1[1¬11]2]2}
Centugubrigoogol, {100,100[1[1¬1,2]2]2}
Big Bird, \(\{100,100 [1 [1 \neg 1 \neg 2] 2] 2\}\)
Extremebixul, 200![1(1)[₂200,200,200,200,200]]
Kiloextremebixul, (200![1(1)[₂200,200,200,200,200]])![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]]
Tria-hierarchaxis, {100,100[1[1[2\₃2]2]2]2}
Bommthet, \(f_{\theta(\Omega_2,0)}(10)\)
Gigantixul, 200![1(1)[₃200,200,200]]
Gigantibixul, 200![1(1)[₃200,200,200,200]]
Ultimate Omega Mega Super Even More Godder Tritri, 3 [3 {3 /// 3} 3] 3
Gigantitrixul, 200![1(1)[₃200,200,200,200,200]]
Gigantiquaxul, 200![1(1)[₃200,200,200,200,200,200]]
Tetra-hierarchaxis, {100,100[1[1[1[2\₄2]2]2]2]2}
Trommthet, \(f_{\theta(\Omega_3,0)}(10)\)
Godly Ultimate Omega Mega Super Even More Godder Tritri, 3 [3 {3 <<<3 <<<3 /// 3>>> 3>>> 3} 3] 3
Penta-hierarchaxis, {100,100[1[1[1[1[2\₅2]2]2]2]2]2}
Quadrommthet, \(f_{\theta(\Omega_4,0)}(10)\)
Hexa-hierarchaxis, {100,100[1[1[1[1[1[2\₆2]2]2]2]2]2]2}
Quintommthet, \(f_{\theta(\Omega_5,0)}(10)\)
Hepta-hierarchaxis, {100,100[1[1[1[1[1[1[2\₇2]2]2]2]2]2]2]2}
Sextommthet, \(f_{\theta(\Omega_6,0)}(10)\)
Octa-hierarchaxis, {100,100[1[1[1[1[1[1[1[2\₈2]2]2]2]2]2]2]2]2}
Septommthet, \(f_{\theta(\Omega_7,0)}(10)\)
Enna-hierarchaxis, {100,100[1[1[1[1[1[1[1[1[2\₉2]2]2]2]2]2]2]2]2]2}
Octommthet, \(f_{\theta(\Omega_8,0)}(10)\)
Deka-hierarchaxis, {100,100[1[1[1[1[1[1[1[1[1[2\₁₀2]2]2]2]2]2]2]2]2]2]2}
Nonommthet, \(f_{\theta(\Omega_9,0)}(10)\)
Dekommthet, \(f_{\theta(\Omega_{10},0)}(10)\)
SCG(13) (lower bound), \(\approx f_{\psi(\Omega_\omega)}(13)\)
Corporalmax / hecta-hierarchaxis, {100,100[1[2\_1,22]2]2}
Hektommthet, \(f_{\theta(\Omega_{100},0)}(10)\)
Meeting point of the three hierarchies, \(f_{\theta(\Omega_{\omega})}(100)\)
Nucleabixul, 200![_{[₂₀₀200]}200]
Kilommthet, \(f_{\theta(\Omega_{1000},0)}(10)\)
Megommthet, \(f_{\theta(\Omega_{10^6},0)}(10)\)
Gigommthet, \(f_{\theta(\Omega_{10^9},0)}(10)\)
Terommthet, \(f_{\theta(\Omega_{10^{12}},0)}(10)\)
Petommthet, \(f_{\theta(\Omega_{10^{15}},0)}(10)\)
Exommthet, \(f_{\theta(\Omega_{10^{18}},0)}(10)\)
Zettommthet, \(f_{\theta(\Omega_{10^{21}},0)}(10)\)
Yottommthet, \(f_{\theta(\Omega_{10^{24}},0)}(10)\)

\(f_{\psi_0(\Omega_\omega)}^2(10)\) ~ \(f_{\psi_0(\Phi(1,0))+1}(10)\)[]

Pair sequence number, \(\approx f_{\psi(\Omega_\omega)+1}(10)\)
Stage array number, \(\approx f_{\psi(\Omega_{\omega})+1}(100)\)
Mulporalmax, {100,100[1[1[2\_2,22]2]2]2}
Big Chunk, {10,100 [1 [1 [1 \_2,2 3] 2] 2] 2}
Powporalmax, {100,100[1[1[1[2\_3,22]2]2]2]2}
Corplodalmax, {100,100[1[1[2\_1,32]2]2]2}
Absolutely Godly Ultimate Omega Mega Super Even More Godder Tritri, 3 [3 {3 \ 3, 3} 3] 3
Cordetalmax, {100,100[1[1[1[2\_1,42]2]2]2]2}
Meg-Googolmax, {100,100[1[2\_1,1,22]2]2}
Dumeg-Googolmax, {100,100[1[1[2\_1,1,32]2]2]2}
Gig-Googolmax, {100,100[1[2\_1,1,1,22]2]2}
Dugig-Googolmax, {100,100[1[1[2\_1,1,1,32]2]2]2}
Ter-Googolmax, {100,100[1[2\_1,1,1,1,22]2]2}
Goobolmax, {100,100[1[2\_1[2]22]2]2}
Gibbolmax, {100,100[1[1[2\_2[2]22]2]2]2}
Gootrolmax, {100,100[1[1[2\_1[2]32]2]2]2}
Gooterolmax, {100,100[1[1[1[2\_1[2]42]2]2]2]2}
Diteralmax / dubolmax, {100,100[1[2\_1[2]1[2]22]2]2}
Xappolmax, {100,100[1[2\_1[3]22]2]2}
Colossolmax, {100,100[1[2\_1[4]22]2]2}
Goplexulusmax, {100,100[1[2\_1[1[2]2]22]2]2}
Bimixommwil, \(f_{\psi(\Omega_{\psi(\Omega)})}(10)\)
Tethrinoogolmax, {100,100[1[2\_1[1\2]22]2]2}
Tethrinoofactimax / hecto-tethrinoogolmax, {100,100[1[2\_1[2\2]22]2]2}
Terrible tethrinoogolmax, {100,100[1[2\_1[1\3]22]2]2}
Terrible terrible tethrinoogolmax, {100,100[1[2\_1[1\4]22]2]2}
Tethrinoocrossmax, {100,100[1[2\_1[1\1\2]22]2]2}
Secundotethrated-tethrinoocrossmax, {100,100[1[2\_1[1\1\3]22]2]2}
Tethrinoocubormax, {100,100[1[2\_1[1\1\1\2]22]2]2}
Tethrinooteronmax, {100,100[1[2\_{1[1\1\1\1\2]2}2]2]2}
Tethrinootopemax, {100,100[1[2\_{1[1[2\₂2]2]2}2]2]2}
Trimixommwil, \(f_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega)})})}(10)\)
Quadrimixommwil, \(f_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega)})})})}(10)\)
Quintimixommwil, \(f_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega_{\psi(\Omega)})})})})}(10)\)
Sextimixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{6\ \Omega's}}(10)\)
Septimixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{7\ \Omega's}}(10)\)
Octimixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{8\ \Omega's}}(10)\)
Nonimixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{9\ \Omega's}}(10)\)
Dekomixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10\ \Omega's}}(10)\)
Binommwil, \(f_{\psi(\Omega_\Omega)}(10)\)
Hektomixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{100\ \Omega's}}(10)\)
Kilomixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{1000\ \Omega's}}(10)\)
Megomixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^6\ \Omega's}}(10)\)
Gigomixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^9\ \Omega's}}(10)\)
Teromixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{12}\ \Omega's}}(10)\)
Petomixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{15}\ \Omega's}}(10)\)
Exomixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{18}\ \Omega's}}(10)\)
Zettomixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{21}\ \Omega's}}(10)\)
Yottomixommwil, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{24}\ \Omega's}}(10)\)
The HUS, S(U(H(3)))
Grand HUS, S(S(S(U(U(U(H(H(H(3)))))))))
Great HUS, S(S(S( ... (S(U(U(U( ... (U(H(H(H( ... (H(3))) ... ))) (with the HUS number of S's, the HUS number of U's, and the HUS number of H's)
Nucleatrixul, 200![_{[_{[₂₀₀200]}200]}200]
Trinommwil, \(f_{\psi(\Omega_{\Omega_\Omega})}(10)\)
Nucleaquaxul, 200![_{[_{[_{[₂₀₀200]}200]}200]}200]
Quadrinommwil, \(f_{\psi(\Omega_{\Omega_{\Omega_\Omega}})}(10)\)
Quintinommwil, \(f_{\psi(\Omega_{\Omega_{\Omega_{\Omega_\Omega}}})}(10)\)
Sextinommwil, \(f_{\psi(\Omega_{\Omega_{\Omega_{\Omega_{\Omega_\Omega}}}})}(10)\)
Septinommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{7\ \Omega's})}(10)\)
Octinommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{8\ \Omega's})}(10)\)
Noninommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{9\ \Omega's})}(10)\)
Dekinommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10\ \Omega's})}(10)\)
Hektinommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{100\ \Omega's})}(10)\)
Kilinommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{1000\ \Omega's})}(10)\)
Meginommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^6\ \Omega's})}(10)\)
Giginommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^9\ \Omega's})}(10)\)
Terinommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{12}\ \Omega's})}(10)\)
Petinommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{15}\ \Omega's})}(10)\)
Exinommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{18}\ \Omega's})}(10)\)
Zettinommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{21}\ \Omega's})}(10)\)
Yottinommwil, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{24}\ \Omega's})}(10)\)

\(> f_{\psi_0(\Phi_1(0))+1}(10)\)[]

Some of these numbers are based on functions which are neither provable nor disprovable to be total in \(\mathrm{ZFC}\).

Unimah, \(f_{\psi(I)}(10)\)
Bitetrotos, \(f_{\psi(I^I)}(10)\)
Tritetrotos, \(f_{\psi(I^{I^I})}(10)\)
Quadritetrotos, \(f_{\psi(I^{I^{I^I}})}(10)\)
Quintitetrotos, \(f_{\psi(I^{I^{I^{I^I}}})}(10)\)
Sextitetrotos, \(f_{\psi(I\uparrow\uparrow6)}(10)\)
Septitetrotos, \(f_{\psi(I\uparrow\uparrow7)}(10)\)
Octitetrotos, \(f_{\psi(I\uparrow\uparrow8)}(10)\)
Nonitetrotos, \(f_{\psi(I\uparrow\uparrow9)}(10)\)
Dekotetrotos, \(f_{\psi(I\uparrow\uparrow10)}(10)\)
Hektotetrotos, \(f_{\psi(I\uparrow\uparrow100)}(10)\)
Kilotetrotos, \(f_{\psi(I\uparrow\uparrow1000)}(10)\)
Megotetrotos, \(f_{\psi(I\uparrow\uparrow10^6)}(10)\)
Gigotetrotos, \(f_{\psi(I\uparrow\uparrow10^9)}(10)\)
Terotetrotos, \(f_{\psi(I\uparrow\uparrow10^{12})}(10)\)
Petotetrotos, \(f_{\psi(I\uparrow\uparrow10^{15})}(10)\)
Exotetrotos, \(f_{\psi(I\uparrow\uparrow10^{18})}(10)\)
Zettotetrotos, \(f_{\psi(I\uparrow\uparrow10^{21})}(10)\)
Yottotetrotos, \(f_{\psi(I\uparrow\uparrow10^{24})}(10)\)
Uninotos, \(f_{\psi(I_I)}(10)\)
Binotos, \(f_{\psi(I_{I_I})}(10)\)
Trinotos, \(f_{\psi(I_{I_{I_I}})}(10)\)
Sextinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{7\ I's})}(10)\)
Dekinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{11\ I's})}(10)\)
Hektinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{101\ I's})}(10)\)
Kilinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{1001\ I's})}(10)\)
Meginotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^6+1\ I's})}(10)\)
Giginotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^9+1\ I's})}(10)\)
Terinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{12}+1\ I's})}(10)\)
Petinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{15}+1\ I's})}(10)\)
Exinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{18}+1\ I's})}(10)\)
Zettinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{21}+1\ I's})}(10)\)
Yottinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{24}+1\ I's})}(10)\)
Kumakuma 3 variables ψ number, F^10¹⁰⁰(10¹⁰⁰)
Bimah, \(f_{\psi(I(2,0))}(10)\)
Trimah, \(f_{\psi(I(3,0))}(10)\)
Quadrimah, \(f_{\psi(I(4,0))}(10)\)
Quintimah, \(f_{\psi(I(5,0))}(10)\)
Sextimah, \(f_{\psi(I(6,0))}(10)\)
Septimah, \(f_{\psi(I(7,0))}(10)\)
Octimah, \(f_{\psi(I(8,0))}(10)\)
Nonimah, \(f_{\psi(I(9,0))}(10)\)
Dekimah, \(f_{\psi(I(10,0))}(10)\)
Hektimah, \(f_{\psi(I(100,0))}(10)\)
Kilimah, \(f_{\psi(I(1000,0))}(10)\)
Megimah, \(f_{\psi(I(10^6,0))}(10)\)
Gigimah, \(f_{\psi(I(10^9,0))}(10)\)
Terimah, \(f_{\psi(I(10^{12},0))}(10)\)
Petimah, \(f_{\psi(I(10^{15},0))}(10)\)
Eximah, \(f_{\psi(I(10^{18},0))}(10)\)
Zettimah, \(f_{\psi(I(10^{21},0))}(10)\)
Yottimah, \(f_{\psi(I(10^{24},0))}(10)\)
Uninimah, \(f_{\psi(I(I(0,0),0))}(10)\)
Binimah, \(f_{\psi(I(I(I(0,0),0),0))}(10)\)
Trinimah, \(f_{\psi(I(I(I(I(0,0),0),0),0))}(10)\)
Quadrinimah, \(f_{\psi(I(I(I(I(I(0,0),0),0),0),0))}(10)\)
Quintinimah, \(f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{6\ I's})}(10)\)
Sextinimah, \(f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{7\ I's})}(10)\)
Septinimah, \(f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{8\ I's})}(10)\)
Terinimah, \(f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{10^{12}+1\ I's})}(10)\)
Zettinimah, \(f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{10^{21}+1\ I's})}(10)\)
Yottinimah, \(f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{10^{24}+1\ I's})}(10)\)
グラハム数ver ε.0.1.0 (Graham's number version ε.0.1.0), G⁶⁴(4)
Tritetremar, \(f_{\psi(M^{M^M})}(10)\)
Sextitetremar, \(f_{\psi(M\uparrow\uparrow6)}(10)\)
Terotetremar, \(f_{\psi(M\uparrow\uparrow10^{12})}(10)\)
Petotetremar, \(f_{\psi(M\uparrow\uparrow10^{15})}(10)\)
Exotetremar, \(f_{\psi(M\uparrow\uparrow10^{18})}(10)\)
Zettotetremar, \(f_{\psi(M\uparrow\uparrow10^{21})}(10)\)
Yottotetremar, \(f_{\psi(M\uparrow\uparrow10^{24})}(10)\)
Uninemar, \(f_{\psi(M_M)}(10)\)
Trinemar, \(f_{\psi(M_{M_{M_M}})}(10)\)
Quadrinemar, \(f_{\psi(M_{M_{M_{M_M}}})}(10)\)
Quintinemar, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{6\ M's})}(10)\)
Sextinemar, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{7\ M's})}(10)\)
Kilinemar, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{1001\ M's})}(10)\)
Meginemar, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^6+1\ M's})}(10)\)
Giginemar, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^9+1\ M's})}(10)\)
T erinemar, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{12}+1\ M's})}(10)\)
Petinemar, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{15}+1\ M's})}(10)\)
Exinemar, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{18}+1\ M's})}(10)\)
Zettinemar, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{21}+1\ M's})}(10)\)
Yottinemar, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{24}+1\ M's})}(10)\)
Uninamus, \(f_{\psi(M(M(0;0);0))}(10)\)
Meginamus, \(f_{\psi(\underbrace{M(M(\cdots M(0;0)\cdots;0);0)}_{10^{6}+1\ M's})}(10)\)
Exinamus, \(f_{\psi(\underbrace{M(M(\cdots M(0;0)\cdots;0);0)}_{10^{18}+1\ M's})}(10)\)
Yottinamus, \(f_{\psi(\underbrace{M(M(\cdots M(0;0)\cdots;0);0)}_{10^{24}+1\ M's})}(10)\)
Tritar, \(f_{C(C(C(\Omega_{3}2,0),0),0)}(3) = Tar(3)\)
Quadritar, \(f_{C(C(C(C(\Omega_{4}2,0),0),0),0)}(4) = Tar(4)\)
Quintitar, \(f_{C(C(C(C(C(\Omega_{5}2,0),0),0),0),0)}(5) = Tar(5)\)
Sextitar, \(f_{C(C(C(C(C(C(\Omega_{6}2,0),0),0),0),0),0)}(6) = Tar(6)\)
Septitar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{7}2,0),0),\cdots ),0)}_{7\text{ C's}}}(7) = Tar(7)\)
Octitar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{8}2,0),0),\cdots ),0)}_{8\text{ C's}}}(8) = Tar(8)\)
Nonitar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{9}2,0),0),\cdots ),0)}_{9\text{ C's}}}(9) = Tar(9)\)
Dekotar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{10}2,0),0),\cdots ),0)}_{10\text{ C's}}}(10) = Tar(10)\)
Hektotar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{100}2,0),0),\cdots ),0)}_{100\text{ C's}}}(100) = Tar(100)\)
Kilotar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{1000}2,0),0),\cdots ),0)}_{1000\text{ C's}}}(1000) = Tar(1000)\)
Megotar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{6}}2,0),0),\cdots ),0)}_{10^{6}\text{ C's}}}(10^{6}) = Tar(10^{6})\)
Gigotar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{9}}2,0),0),\cdots ),0)}_{10^{9}\text{ C's}}}(10^{9}) = Tar(10^{9})\)
Terotar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{12}}2,0),0),\cdots ),0)}_{10^{12}\text{ C's}}}(10^{12}) = Tar(10^{12})\)
Petotar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{15}}2,0),0),\cdots ),0)}_{10^{15}\text{ C's}}}(10^{15}) = Tar(10^{15})\)
Exotar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{18}}2,0),0),\cdots ),0)}_{10^{18}\text{ C's}}}(10^{18}) = Tar(10^{18})\)
Zettotar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{21}}2,0),0),\cdots ),0)}_{10^{21}\text{ C's}}}(10^{21}) = Tar(10^{21})\)
Yottotar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{10^{24}}2,0),0),\cdots ),0)}_{10^{24}\text{ C's}}}(10^{24}) = Tar(10^{24})\)
Unintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{\text{Dekotar}}2,0),0),\cdots ),0)}_{\text{Dekotar C's}}}(\text{Dekotar}) = Tar(Dekotar) = Tar(Tar)\)
Bintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{\text{Unintar}}2,0),0),\cdots ),0)}_{\text{Unintar C's}}}(\text{Unintar}) = Tar(Tar(Tar)) = Tar(Tar(Dekotar))\)
Trintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{\text{Bintar}}2,0),0),\cdots ),0)}_{\text{Bintar C's}}}(\text{Bintar}) = Tar(Tar(Tar(Tar)))\)
Quadrintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{3\text{-intar}}2,0),0),\cdots ),0)}_{3\text{-intar C's}}}(3\text{-intar}) = Tar^{4}(Tar)\)
Quintintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{4\text{-intar}}2,0),0),\cdots ),0)}_{4\text{-intar C's}}}(4\text{-intar}) = Tar^{5}(Tar)\)
Sextintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{5\text{-intar}}2,0),0),\cdots ),0)}_{5\text{-intar C's}}}(5\text{-intar}) = Tar^{6}(Tar)\)
Septintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{6\text{-intar}}2,0),0),\cdots ),0)}_{6\text{-intar C's}}}(6\text{-intar}) = Tar^{7}(Tar)\)
Octintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{7\text{-intar}}2,0),0),\cdots ),0)}_{7\text{-intar C's}}}(7\text{-intar}) = Tar^{8}(Tar)\)
Nonintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{8\text{-intar}}2,0),0),\cdots ),0)}_{8\text{-intar C's}}}(8\text{-intar}) = Tar^{9}(Tar)\)
Dekintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{9\text{-intar}}2,0),0),\cdots ),0)}_{9\text{-intar C's}}}(9\text{-intar}) = Tar^{10}(Tar)\)
Hektintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{99\text{-intar}}2,0),0),\cdots ),0)}_{99\text{-intar C's}}}(99\text{-intar}) = Tar^{100}(Tar)\)
Kilintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{999\text{-intar}}2,0),0),\cdots ),0)}_{999\text{-intar C's}}}(999\text{-intar}) = Tar^{1000}(Tar)\)
Megintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{6}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{6}-1)\text{-intar C's}}}((10^{6}-1)\text{-intar}) = Tar^{10^{6}}(Tar)\)
Gigintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{9}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{9}-1)\text{-intar C's}}}((10^{9}-1)\text{-intar}) = Tar^{10^{9}}(Tar)\)
Terintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{12}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{12}-1)\text{-intar C's}}}((10^{12}-1)\text{-intar}) = Tar^{10^{12}}(Tar)\)
Petintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{15}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{15}-1)\text{-intar C's}}}((10^{15}-1)\text{-intar}) = Tar^{10^{15}}(Tar)\)
Exintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{18}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{18}-1)\text{-intar C's}}}((10^{18}-1)\text{-intar}) = Tar^{10^{18}}(Tar)\)
Zettintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{21}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{21}-1)\text{-intar C's}}}((10^{21}-1)\text{-intar}) = Tar^{10^{21}}(Tar)\)
Yottintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{(10^{24}-1)\text{-intar}}2,0),0),\cdots ),0)}_{(10^{24}-1)\text{-intar C's}}}((10^{24}-1)\text{-intar}) = Tar^{10^{24}}(Tar)\)
Tarintar, \(f_{\underbrace{C(C(\cdots(C(C(\Omega_{(Dekotar-1)\text{-intar}}2,0),0),\cdots ),0)}_{(Dekotar-1)\text{-intar C's}}}((Dekotar-1)\text{-intar}) = Tar^{Tar}(Tar)\)
Loader's number (output of loader.c), \(D^5(99)\)
Bashicu matrix number with respect to Bashicu matrix system version 2.3
６ (N primitive)
Y sequence number, \(f^{2000}(1)\)
\(\omega\)-Y sequence number, \(f^{2000}(1)\) using f(n)=\(\omega\)-Y\((1,\omega)[n]\)

Stronger set theory level[]

These numbers are based on functions which are not provably total in \(\mathrm{ZFC}\), but based on functions that are known to be provably total in stronger set theories.

the least transcendental integer, The Well-Definedness of the least transcendental integer is non-trivial, as we do not have a proof of the \(\Sigma_1\)-soundness of \(\textrm{ZFC}\) set theory by Goedel's incompleteness theorem.
Yudkowsky's number, ill-defined

Larger numbers

List of googolisms/Higher computable level

Contents

\(f_{\psi_0(\Omega_2)}^2(10)\) ~ \(f_{\psi_0(\Omega_\omega)}^2(10)\)[]

\(f_{\psi_0(\Omega_\omega)}^2(10)\) ~ \(f_{\psi_0(\Phi(1,0))+1}(10)\)[]

\(> f_{\psi_0(\Phi_1(0))+1}(10)\)[]

Stronger set theory level[]

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