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Hyper-Moser notation
TypeHierarchy
Growth rate\(f_{\omega^\omega}(n)\)

The Hyper-Moser notation is an extension of Steinhaus-Moser notation invented by Aarex Tiaokhiao.[1] Formally it is defined as follows:

\(M(n,m \#) = \underbrace{M(M(M(...,m-1\#),m-1\#),m-1\#)}_{n~M\text s}\) (\(m>1\))

\(M(n,1) = n^n\) (only 2 entries and \(m=1\)), or n in a triangle = triangle(n).

\(M(\#\ 0) = M(\#)\) (last entry is 0)

\(M(n,0,0,...,0,0,m) = M(\underbrace{n,n...n,n}_{n+1},m-1)\) (otherwise)

EtymologyEdit

The M stands for Moser.

Examples Edit

\(M(n,2) = n\) in a square

\(M(n,3) = n\) in a circle or pentagon

\(M(2,3) =\) Mega

\(M(n,m) = n\) in a (2+m)-gon

\(M(2,M(2,3)-2) =\) Moser

\(M(n,0,1) = M(n,n)\)

\(M(2,1,1) = M(M(2,0,1),0,1) = M(M(2,2),0,1) = M(256,256)\)

\(M(3,1,1) = M(M(M(3,0,1),0,1),0,1) = M(M(M(3,3),0,1),0,1) = M(M(M(3,3),M(3,3)),0,1) = M(M(M(3,3),M(3,3)),M(M(3,3),M(3,3)))\)

\(M(65,1,1) > G\) where G is Graham's Number

\(M(2,2,1) = M(M(256,256),1,1)\)

\(M(3,2,1) = M(M(M(M(M(3,3),M(3,3)),M(M(3,3),M(3,3))),1,1),1,1)\)

\(M(2,3,1) = M(M(2,2,1),2,1)\)

\(M(n,0,2) = M(n,n,1)\)

SourcesEdit

  1. Tiaokhiao, AarexHyper-Moser notation. Retrieved 2013-03-30.

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