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.[1] 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*}

The last four digits of a Moser are ...1056.

Tim Chow proved that Graham's number is much larger than Moser.[2] 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.[3] 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.

Sources Edit

  1. Moser
  2. Proof that G >> M. (This website uses \(n[m]_p\) = n inside p m-gons for Steinhaus-Moser Notation.)
  3. [1]

See also Edit

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