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 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. 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.

\(f_{\psi(\varepsilon_{\Omega+1})}(10^6)\) ~ \(f_{\psi(\Omega_\omega)}(10^{10^6})\)

• Megotetrommthet, \(f_{\theta(\Omega\uparrow\uparrow10^6,0)}(10)\)
• Gigotetrommthet, \(f_{\theta(\Omega\uparrow\uparrow10^9,0)}(10)\)
• Terotetrommthet, \(f_{\theta(\Omega\uparrow\uparrow10^{12},0)}(10)\)
• Petotetrommthet, \(f_{\theta(\Omega\uparrow\uparrow10^{15},0)}(10)\)
• Exotetrommthet, \(f_{\theta(\Omega\uparrow\uparrow10^{18},0)}(10)\)
• Zettotetrommthet, \(f_{\theta(\Omega\uparrow\uparrow10^{21},0)}(10)\)
• Yottotetrommthet, \(f_{\theta(\Omega\uparrow\uparrow10^{24},0)}(10)\)
• 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, \(f_{\theta(\Omega_8,0)}(10)\)
• 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}
• 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, \(f_{\theta(\Omega_{10^{24}},0)}(10)\)

\(f_{\psi(\Omega_\omega)}(10^{10^6})\) ~ \(f_{\psi(\psi_I(0))}(10^6)\)

• 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}
• Super gongulus, {10,10 (100) 2 / 2}
• Wompogulus, {10,10 (10) 2 / 100}
• Guapamonga, 10¹⁰⁰ && (10¹⁰⁰ & 10)
• Guapamongaplex, 10^guapamonga && (10^guapamonga & 10)
• 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, \(f_{\psi(\underbrace{\Omega_{\Omega_{\cdots_\Omega}}}_{10^6\ \Omega's})}(10)\)

\(>f_{\psi(\psi_I(0))}(10^6)\)

• 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, \(\lbrace \text{big hoss},\text{big hoss} \underbrace{///\cdots ///}_{\text{big hoss}} 2\rbrace\)
• 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, \(f_{\psi(\underbrace{M(M(\cdots M(0;0)\cdots;0);0)}_{10^{24}+1\ M's})}(10)\)
• Goshomity, \(\lbrace L2,100\rbrace_{100,100} = \lbrace 100,100 \underbrace{\backslash\backslash\backslash\cdots\backslash\backslash\backslash}_{100} 2\rbrace\)
• Good goshomity, \(\{100,100 \underbrace{\backslash\backslash\backslash\backslash\ldots\backslash\backslash\backslash\backslash}_{\text{Goshomity}} 2\}\)
• Big Bukuwaha, \(\lbrace L2,X\rbrace_{100,100}\), where X is a Bukuwaha array.
• Bongo Bukuwaha, \(\lbrace L3,X\rbrace_{100,100}\), where X is a Big Bukuwaha array.
• Quabinga Bukuwaha, \( \lbrace L4,X\rbrace_{100,100}\), where X is a Bongo Bukuwaha array.
• Meameamealokkapoowa, \(\{\text{L}100,10\}_{10,10}\)
• Meameamealokkapoowa-arrowa, \(\{\text{meameamealokkapoowa},2,1,2\}\)
• Aarex's meameamealokkapoowa-oompa, \(\{LLL \ldots LLL,10\}_{10,10}\) where there are meameamealokkapoowa L's
• Meameamealokkapoowa oompa, \(\{LLL \ldots A \ldots LLL,10\}_{10,10}\), A is a meameamealokkapoowa array of L's
• 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)
• the least transcendental integer
• Yudkowsky's number

Larger numbers