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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.

\(f_{\psi_0(\Omega_2)}^2(10)\) ~ \(f_{\psi_0(\Omega_\omega)}^2(10)\)[]

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

  • 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.

Larger numbers

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