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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.

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

• Pair sequence number, $$\approx f_{\psi(\Omega_\omega)+1}(10)$$
• 段階配列数, $$\approx f_{\psi(\Omega_{\omega})+1}(100)$$
• 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
• (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.