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

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

• 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]]
• 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, \(f_{\theta(\Omega_8,0)}(10)\)
• Nonommthet, \(f_{\theta(\Omega_9,0)}(10)\)
• Dekommthet, \(f_{\theta(\Omega_{10},0)}(10)\)
• Hektommthet, \(f_{\theta(\Omega_{100},0)}(10)\)
• 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, \(f_{\theta(\Omega_{10^{24}},0)}(10)\)

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

• SCG(13) (lower bound)
• Pair sequence number, \(\approx f_{\psi(\Omega_\omega)+1}(10)\)
• 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]]
• Bimah, \(f_{\psi(I(2,0))}(10)\)
• 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
• 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)
• Loader's number (Output of loader.c), \(D^5(99)\)

Larger numbers