| Hyper-Moser notation | |
|---|---|
| Type | Hierarchy |
| Growth rate | \(f_{\omega^\omega}(n)\) |
Hyper-Moser notation is an extension of Steinhaus-Moser notation invented by Aarex Tiaokhiao.[1] Formally it is defined as follows:
- Let \(\#\) denote the unchained remainder of the arguments.
- \(M(n,m \#) = \underbrace{M(M(M(...,m-1\#),m-1\#),m-1\#)}_{n~M\text s}\) (\(m>1\))
- \(M(n,1) = n^n\) (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)
Etymology[]
The M stands for Moser.
Examples[]
\(M(n,2) = n\) 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
\(M(n,0,1) = M(n,n)\)
\(M(2,1,1) = M(M(2,0,1),0,1) = M(M(2,2),0,1) = M(256,256)\)
\(M(3,1,1) = M(M(M(3,0,1),0,1),0,1) = M(M(M(3,3),0,1),0,1) = M(M(M(3,3),M(3,3)),0,1) = M(M(M(3,3),M(3,3)),M(M(3,3),M(3,3)))\)
\(M(65,1,1) >\) Graham's Number
\(M(2,2,1) = M(M(256,256),1,1)\)
\(M(3,2,1) = M(M(M(M(M(3,3),M(3,3)),M(M(3,3),M(3,3))),1,1),1,1)\)
\(M(2,3,1) = M(M(2,2,1),2,1)\)
\(M(n,0,2) = M(n,n,1)\)Sources[]
- ↑ Tiaokhiao, Aarex. Hyper-Moser notation. Retrieved 2013-03-30.