List of googolisms/Higher computable level

List of googolisms

• Class 0 and 1
• Class 2
• Class 3
• Class 4
• Class 5
• Tetration level
• Up-arrow notation level
• Linear omega level
• Quadratic omega level
• Polynomial omega level
• Exponentiated linear omega level
• Exponentiated polynomial omega level
• Double exponentiated polynomial omega level
• Triple exponentiated polynomial omega level
• Iterated Cantor normal form level
• Epsilon level
• Binary phi level
• Bachmann's collapsing level
• Higher computable level
• Uncomputable numbers

Smaller numbers

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 BEAF numbers beyond tetrational arrays, which are ill-defined, 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.

\(f_{\psi_0(\varepsilon_{\Omega+1})}^2(10)\) ~ \(f_{\psi_0(\Omega_\omega)}^2(10)\)

• 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]]
• Bommthet, \(f_{\theta(\Omega_2,0)}(10)\)
• Gigantixul, 200![1(1)[₃200,200,200]]
• Golapulusplex, {10,100} & 10 & 10 & 10
• 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]]
• Trommthet, \(f_{\theta(\Omega_3,0)}(10)\)
• Quadrommthet, \(f_{\theta(\Omega_4,0)}(10)\)
• Quintommthet, \(f_{\theta(\Omega_5,0)}(10)\)
• Sextommthet, \(f_{\theta(\Omega_6,0)}(10)\)
• Septommthet, \(f_{\theta(\Omega_7,0)}(10)\)
• Octommthet, \(f_{\theta(\Omega_8,0)}(10)\)
• Dekulus / Big Mac, {10,10/2}
• Nonommthet, \(f_{\theta(\Omega_9,0)}(10)\)
• Dekommthet, \(f_{\theta(\Omega_{10},0)}(10)\)
• SCG(13) (lower bound), \(\approx f_{\psi(\Omega_\omega)}(13)\)
• Hektommthet, \(f_{\theta(\Omega_{100},0)}(10)\)
• The Whopper, {10,100/2}
• Meeting point of the three hierarchies, \(f_{\theta(\Omega_{\omega})}(100)\) = \( f_{\psi_0(\psi_{\omega}^3(0))}(100)\)^{[citation needed]}
• 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, \(\approx f_{\psi(\Omega_\omega)+1}(10)\)
• 段階配列数, \(\approx f_{\psi(\Omega_{\omega})+1}(100)\)
• Big boowa, {3,3,3 / 2}
• Great big boowa, {3,3,4 / 2}
• Grand boowa, {3,3,big boowa / 2} = {3,2,2,2 / 2}
• Gigantic big boowa, {3, 3, {3, 3, 4 / 2} / 2} = {3, 3, great big boowa / 2}
• Gorged boowa, {3, 3, {3, 3, {3, 3, 3 / 2} / 2} / 2} = {3, 3, grand boowa / 2}
• Gulp big boowa, {3, 3, {3, 3, {3, 3, 4 / 2} / 2} / 2} = {3, 3, gigantic big boowa / 2}
• Super gongulus, {10,10 (100) 2 / 2}
• Wompogulus, {10,10 (10) 2 / 100}
• Guapamonga, 10¹⁰⁰ && (10¹⁰⁰ & 10)
• Guapamongaplex, 10^guapamonga && (10^guapamonga & 10)
• Big Chunk, {10,100 [1 [1 [1 \_2,2 3] 2] 2] 2}
• Bimixommwil, \(f_{\psi(\Omega_{\psi(\Omega)})}(10)\)
• 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, \(f_{\underbrace{\psi(\Omega_{\psi(\Omega_{\cdots_{\psi(\Omega)}\cdots})})}_{10^{24}\ \Omega's}}(10)\)
• 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, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{100\ \Omega's})}(10)\)
• Big hoss, \(\lbrace 100,100 \underbrace{///\cdots ///}_{100} 2\rbrace\)
• Grand hoss, \(\lbrace 100,100 \underbrace{///\cdots ///}_{100} 100\rbrace\)
• 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, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^{24}\ \Omega's})}(10)\)
• Great big hoss, \(\lbrace \text{big hoss},\text{big hoss} \underbrace{///\cdots ///}_{\text{big hoss}} 2\rbrace\)

\(f_{\psi_0(\Phi_1(0))+1}(10)\) ~

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, \(f_{\psi(I^I)}(10)\)
• Bukuwaha, {L,100¹⁰⁰}_100,100
• 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, \(f_{\psi(I\uparrow\uparrow10^{24})}(10)\)
• BIGG, 200? = 200![[_{<1(200)2>⁅200⁆}1]]
• Uninotos, \(f_{\psi(I_I)}(10)\)
• Binotos, \(f_{\psi(I_{I_I})}(10)\)
• Trinotos, \(f_{\psi(I_{I_{I_I}})}(10)\)
• Sextinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{7\ I's})}(10)\)
• Bimah, \(f_{\psi(I(2,0))}(10)\)
• Dekinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{11\ I's})}(10)\)
• Zettinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{21}+1\ I's})}(10)\)
• Yottinotos, \(f_{\psi(\underbrace{I_{I_{\cdots_I}}}_{10^{24}+1\ I's})}(10)\)
• 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, \(f_{\psi(I(I(0,0),0))}(10)\)
• Trinimah, \(f_{\psi(I(I(I(I(0,0),0),0),0))}(10)\)
• 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, \(f_{\psi(\underbrace{I(I(\cdots I(0,0)\cdots,0),0)}_{10^{24}+1\ I's})}(10)\)
• 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, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^9+1\ M's})}(10)\)
• Terinemar, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^{12}+1\ M's})}(10)\)
• 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, \(f_{\psi(M(M(0;0);0))}(10)\)
• Zettinamus, \(f_{\psi(\underbrace{M(M(\cdots M(0;0)\cdots;0);0)}_{10^{21}+1\ M's})}(10)\)
• Yottinamus, \(f_{\psi(\underbrace{M(M(\cdots M(0;0)\cdots;0);0)}_{10^{24}+1\ M's})}(10)\)
• Kumakuma 3 variables ψ number, F¹⁰¹⁰⁰(10¹⁰⁰)
• グラハム数ver ε.0.1.0, G⁶⁴(4)
• Tritar, Tar(3)
• Quadritar, Tar(4)
• Quintitar, Tar(5)
• Sextitar, Tar(6)
• Septitar, Tar(7)
• Octitar, Tar(8)
• Nonitar, Tar(9)
• Dekotar, Tar(10)
• Hektotar, Tar(100)
• Kilotar, Tar(1000)
• Megotar, Tar(10⁶)
• Gigotar, Tar(10⁹)
• Terotar, Tar(10¹²)
• Petotar, Tar(10¹⁵)
• Exotar, Tar(10¹⁸)
• Zettotar, Tar(10²¹)
• Yottotar, Tar(10²⁴)
• Unintar, Tar(Dekotar) = Tar(Tar)
• Bintar, Tar(Tar(Dekotar)) = Tar(Tar(Tar))
• Trintar, Tar(Tar(Tar(Tar)))
• Quadrintar, Tar⁴(Tar)
• Quintintar, Tar⁵(Tar)
• Sextintar, Tar⁶(Tar)
• Septintar, Tar⁷(Tar)
• Octintar, Tar⁸(Tar)
• Nonintar, Tar⁹(Tar)
• Dekintar, Tar¹⁰(Tar)
• Hektintar, Tar¹⁰⁰(Tar)
• Kilintar, Tar¹⁰⁰⁰(Tar)
• Megintar, Tar¹⁰⁶(Tar)
• Gigintar, Tar¹⁰⁹(Tar)
• Terintar, Tar¹⁰¹²(Tar)
• Petintar, Tar¹⁰¹⁵(Tar)
• Exintar, Tar¹⁰¹⁸(Tar)
• Zettintar, Tar¹⁰²¹(Tar)
• Yottintar, Tar¹⁰²⁴(Tar)
• Tarintar, 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, f²⁰⁰⁰(1)

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
• Yudkowsky's number

Larger numbers