List of googolisms/Higher computable level

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 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]22]2]2}
*Tethrinootopemax, {100,100[1[2\1[1[2\22]2]22]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, F10100(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, \(f_{\psi(\underbrace{M_{M_{\cdots_M}}}_{10^9+1\ M's})}(10)\)
*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, \(f_{\psi(M(M(0;0);0))}(10)\)
*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
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