Moser

Moser's number, often abbreviated to just Moser, is equal to 2 inside a mega-gon, where Steinhaus-Moser Notation is used or M(2,M(2,3)-2) or M(2,Mega-2) in Hyper-Moser notation.Moser Formally:
\begin{eqnarray*}
S_3(n) &=& n^n \\
S_{k + 1}(n) &=& S_k^n(n) \\
\text{Moser} &=& S_{S_5(2)}(2) \\
\end{eqnarray*}
Allam A. states that the last 8 digits of the Moser are ...80301056.Allam A. Steinhaus-Moser Notation retrieved 2023-01-17.
Tim Chow proved that Graham's number is much larger than Moser.Proof that G >> M. (This website uses \(n[m]_p\) = n inside p m-gons for Steinhaus-Moser Notation.) The proof hinges on the fact that, using Steinhaus-Moser Notation, n in a (k + 2)-gon is less than \(n\underbrace{\uparrow\uparrow\ldots\uparrow\uparrow}_{2k-1}n\). He sent the proof to Susan Stepney on July 7, 1998. Coincidentally, Stepney was sent a similar proof by Todd Cesere several days later.
Matt Hudelson incorrectly defines a Moser as 2 inside a "Mega + 2"-gon, using his own slightly different version of Steinhaus-Moser Notation.
== Note about source ==
It is well-known as Moser, but no source of this number or Steinhaus-Moser Notation written by Moser can be found. For example, in the Wikipedia article of (in the version of 19 July 2023), it is described that Leo Moser is best known for his polygon notation, but the article does not describe his publication about the polygon notation. In MathWorld, Moser is described without source. It is "well-known" but not cited anywhere.Talk:Moser#Source If someone finds a source by Moser himself, please add information about it.
== Sources ==
== See also ==
*A-ooga
*Leo Moser
*Graham's Number
*Mega
*Megiston
*Steinhaus-Moser Notation
ja:モーザー数
Category:Numbers
Category:Eponymous numbers
Category:Hyper-Moser numbers
Category:Powers of 2
Category:Linear omega level