FANDOM


Welcome to the Master Analysis of Separator Matrix Notation! Currently, the analysis contains parts of SMN that have not been defined yet.


Analysis

Separator Matrix Notation Paraseg Cluster & Limit Indicators Approx FGH & Comparables
(0) \(f_3(n)\) - Tetration
(0) (0) \(f_4(n)\) - Pentation
(0) (0) (0) \(f_5(n)\) - Hexation
(0) (0) (0) (0) \(f_6(n)\) - Heptation
(0) (0) (0) (0) (0) \(f_7(n)\) - Octation
(0)(0) \(f_\omega(n)\) - Arrow NotationAckermann FunctionHyper-E NotationSteinhaus-Moser NotationBasic R Function
(0)(0) (0) \(f_{\omega+1}(n)\) - Expansion
(0)(0) (0) (0) \(f_{\omega+2}(n)\) - Multiexpansion
(0)(0) (0)(0) \(f_{\omega2}(n)\)
(0)(0) (0)(0) (0) \(f_{\omega2+1}(n)\) - Explosion
(0)(0) (0)(0) (0)(0) \(f_{\omega3}(n)\) - Detonation
(0)(0) (0)(0) (0)(0) (0)(0) \(f_{\omega4}(n)\) - Pentonation
(0)(0)(0) \(f_{\omega^2}(n)\)
(0)(0)(0) (0) \(f_{\omega^2+1}(n)\) - Megotion
(0)(0)(0) (0)(0) \(f_{\omega^2+\omega}(n)\) - Megoexpansion
(0)(0)(0) (0)(0)(0) \(f_{\omega^22}(n)\) - Gigotion
(0)(0)(0)(0) \(f_{\omega^3}(n)\)
(0)(0)(0)(0)(0) \(f_{\omega^4}(n)\)
(0)(0)(0)(0)(0)(0) \(f_{\omega^5}(n)\)
(1) \(f_{\omega^\omega}(n)\) - Linear Array NotationExtended Hyper-E Notation
(1) (0) \(f_{\omega^\omega+1}(n)\)
(1) (0)(0)

\(f_{\omega^\omega+\omega}(n)\)

(1) (1) \(f_{\omega^\omega2}(n)\)
(1)(0) \(f_{\omega^{\omega+1}}(n)\)
(1)(0)(0) \(f_{\omega^{\omega+2}}(n)\)
(1)(0)(0)(0) \(f_{\omega^{\omega+3}}(n)\)
(1)(0)(1) \(f_{\omega^{\omega2}}(n)\)
(1)(0)(1)(0) \(f_{\omega^{\omega2+1}}(n)\)
(1)(0)(1)(0)(0) \(f_{\omega^{\omega2+2}}(n)\)
(1)(0)(1)(0)(1) \(f_{\omega^{\omega3}}(n)\)
(1)(0)(1)(0)(1)(0)(1)

\(f_{\omega^{\omega4}}(n)\)

(1)(1) \(f_{\omega^{\omega^2}}(n)\) - Planar Array Notation
(1)(1)(0) \(f_{\omega^{\omega^2+1}}(n)\)
(1)(1)(0)(1) \(f_{\omega^{\omega^2+\omega}}(n)\)
(1)(1)(0)(1)(1) \(f_{\omega^{\omega^22}}(n)\)
(1)(1)(1) \(f_{\omega^{\omega^3}}(n)\)
(1)(1)(1)(1) \(f_{\omega^{\omega^4}}(n)\)
(2) \(f_{\omega^{\omega^\omega}}(n)\) - Dimensional Array Notation
(2)(0) \(f_{\omega^{\omega^\omega}+1}(n)\)
(2)(1) \(f_{\omega^{\omega^\omega+1}}(n)\)
(2)(1)(1) \(f_{\omega^{\omega^\omega+2}}(n)\)
(2)(1)(2) \(f_{\omega^{\omega^\omega+\omega}}(n)\)
(2)(1)(2)(1)(2) \(f_{\omega^{\omega^\omega2}}(n)\)
(2)(2) \(f_{\omega^{\omega^{\omega^2}}}(n)\)
(2)(2)(2) \(f_{\omega^{\omega^{\omega^3}}}(n)\)
(3) \(f_{\omega^{\omega^{\omega^\omega}}}(n)\)
(4) \(f_{\omega^{\omega^{\omega^{\omega^\omega}}}}(n)\)
Limit of bSMN \(f_{\varepsilon_0}(n)\) - Tetrational ArraysHydra FunctionCascading-E NotationGoodstein FunctionBrace NotationBracket Notation
((0)) \(f_{\varepsilon_0}(n)\)
((0)) ((0)) \(f_{\varepsilon_02}(n)\)
((0))(0) \(f_{\varepsilon_0\omega}(n)\)
((0))((0)) \(f_{\varepsilon_0^2}(n)\)
((0))((0))((0)) \(f_{\varepsilon_0^3}(n)\)
((1)) \(f_{\varepsilon_0^\omega}(n)\)
((2)) \(f_{\varepsilon_0^{\omega^\omega}}(n)\)
(((0))) \(f_{\varepsilon_0^{\varepsilon_0}}(n)\)
((((0)))) \(f_{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}(n)\)
(0(0)) \(f_{\varepsilon_1}(n)\)
(0(0))(0(0)) \(f_{\varepsilon_1^2}(n)\)
(0(1)) \(f_{\varepsilon_1^\omega}(n)\)
(0((0))) \(f_{\varepsilon_1^{\varepsilon_0}}(n)\)
(0(((0)))) \(f_{\varepsilon_1^{\varepsilon_0^{\varepsilon_0}}}(n)\)
(1(0)) \(f_{\varepsilon_1^{\varepsilon_1}}(n)\)
(2(0)) \(f_{\varepsilon_1^{\varepsilon_1^{\varepsilon_1}}}(n)\)
((0)(0)) \(f_{\varepsilon_2}(n)\)
(1(0)(0)) \(f_{\varepsilon_2^{\varepsilon_1}}(n)\)
((0)(0)(0)) \(f_{\varepsilon_2^{\varepsilon_2}}(n)\)
((1)") \(f_{\varepsilon_3}(n)\)
((1)(0)) \(f_{\varepsilon_3^{\varepsilon_2}}(n)\)
((1)(0)(1)) \(f_{\varepsilon_3^{\varepsilon_3}}(n)\)
((1)(1)) \(f_{\varepsilon_4}(n)\)
((1)(1)(1)) \(f_{\varepsilon_5}(n)\)

((2)")

\(f_{\varepsilon_\omega}(n)\)
(((0))") \(f_{\varepsilon_{\varepsilon_0}}(n)\)
((((0)))") \(f_{\varepsilon_{\varepsilon_{\varepsilon_0}}}(n)\)
Limit of xSMN \(f_{\zeta_0}(n)\) - X-Sequence Hyper-Exponential Notation
(0,0) \(f_{\zeta_0}(n)\)
(0,0)(0,0)

\(f_{\zeta_0^2}(n)\)

(0,1) \(f_{\zeta_0^\omega}(n)\)
(0,2) \(f_{\zeta_0^{\omega^\omega}}(n)\)
(0,(0)) \(f_{\zeta_0^{\varepsilon_0}}(n)\)
(0,(0,0)) \(f_{\zeta_0^{\zeta_0}}(n)\)
(0,(0,(0,0))) \(f_{\zeta_0^{\zeta_0^{\zeta_0}}}(n)\)
(0,(1,0)) \(f_{\varepsilon_{\zeta_0+1}}(n)\)
(0,(1,(0,0))) \(f_{\varepsilon_{\zeta_0+1}^{\zeta_0}}(n)\)
(0,(1,(1,0))) \(f_{\varepsilon_{\zeta_0+1}^{\varepsilon_{\zeta_0+1}}}(n)\)
(0,(2,0)) \(f_{\varepsilon_{\zeta_0+2}}(n)\)
(0,((0),0)) \(f_{\varepsilon_{\zeta_0+\omega}}(n)\)
(0,((0,0),0)) \(f_{\varepsilon_{\zeta_02}}(n)\)
(0,(((0,0),0),0)) \(f_{\varepsilon_{\zeta_03}}(n)\)
(1,0) \(f_{\varepsilon_{\zeta_0^2}}(n)\)
(2,0) \(f_{\varepsilon_{\zeta_0^22}}(n)\)
((0),0) \(f_{\varepsilon_{\zeta_0^2\omega}}(n)\)
((0,0),0) \(f_{\varepsilon_{\zeta_0^3}}(n)\)
(((0,0),0),0) \(f_{\varepsilon_{\zeta_0^4}}(n)\)
((0,0)) \(f_{\varepsilon_{\zeta_0^\omega}}(n)\)
((0,((0,0)))) \(f_{\varepsilon_{\zeta_0^{\zeta_0}}}(n)\)
((0,((0,((0,0)))))) \(f_{\varepsilon_{\zeta_0^{\zeta_0^{\zeta_0}}}}(n)\)
((0,((1,0)))) \(f_{\varepsilon_{\varepsilon_{\zeta_0+1}}}(n)\)
((0,((2,0)))) \(f_{\varepsilon_{\varepsilon_{\zeta_0+2}}}(n)\)
((0,(((0,0),0)))) \(f_{\varepsilon_{\varepsilon_{\zeta_02}}}(n)\)
((0,((((0,0)),0)))) \(f_{\varepsilon_{\varepsilon_{\zeta_0^\omega}}}(n)\)
((1,0)) \(f_{\zeta_1}(n)\)
((2,0)) \(f_{\zeta_2}(n)\)
(((0,0),0)) \(f_{\zeta_{\zeta_0}}(n)\)
(((1,0)),0)) \(f_{\zeta_{\zeta_1}}(n)\)
(((0,0))) \(f_{\eta_0}(n)\)
(((0,(((1,0)))))) \(f_{\varepsilon_{\eta_0}}(n)\)
(((1,0))) \(f_{\eta_1}(n)\)
((((((0,0))),0))) \(f_{\eta_{\eta_0}}(n)\)
((((0,0)))) \(f_{\phi(4,0)}(n)\)
(((((0,0))))) \(f_{\phi(5,0)}(n)\)
(0,0(0)) \(f_{\phi(\omega,0)}(n)\) - Nested Cascading-E Notation
(0,0(0,0)) \(f_{\phi({\zeta_0},0)}(n)\)
(0,0(0,0(0))) \(f_{\phi(\phi(\omega,0))}(n)\)
Limit of blaSMN \(f_{\Gamma_0}(n)\)
(0,0,0) \(f_{\Gamma_0}(n)\)
(0,0,1) \(f_{\Gamma_0^\omega}(n)\)
(0,1,0) \(f_{\varepsilon_{\Gamma_0+1}}(n)\)
((0),0,0) \(f_{\phi(\omega,0,0)}(n)\) - Extended Cascading-E Notation
(0,0,0,0) \(f_{\phi(1,0,0,0)}(n)\) - Hyper-Extended Cascading-E Notation
(0,0,0,0,0) \(f_{\phi(1,0,0,0,0)}(n)\)
(0,,0) \(f_{\vartheta(\Omega^\omega)}\)

(0,,,0)

\(f_{\vartheta(\Omega^{\vartheta(\Omega^\omega)})}\)
(0(0)0) \(f_{\vartheta(\Omega^\Omega)}\)
(0((0))0) \(f_{\vartheta(\Omega^{\Omega^{\Omega}})}\)
(0(0,0)0) \(f_{\vartheta(\varepsilon_{\Omega+1})}\) - Bird's H Function
(0[0]0) \(f_{\vartheta(\Omega_2)}\)
(0{0}0) \(f_{\vartheta(\Omega_3)}\)
(0-0) \(f_{\vartheta(\Omega_\omega)}\) - Bird's U FunctionBasichuHyudora's Pair Function
(0-(0-0)) \(f_{\vartheta(\Omega_\Omega)}\) - Bird's Array NotationBird's S Function
(0-(0-(0-0))) \(f_{\vartheta(\Omega_{\Omega_\Omega})}\)
(0-(1-0)) \(f_{\psi(\psi_I(0))}\) - Extended Bracket Notation
(1-0) \(f_{\psi(\psi_I(I))}\)
(0-10) \(f_{\psi(\psi_{\varepsilon_{I+1}}(0))}\)
Limit of αSMN \(f_{\psi(\psi_{\chi}(M_M(0)))}\)

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