Steinhaus–Moser notation

In mathematics, Steinhaus–Moser notation is a notation for expressing certain extremely large numbers. It is an extension of Steinhaus's polygon notation.

etc.: $n$ written in an ( $m + 1$ )-sided polygon is equivalent with "the number $n$ inside $n$ nested $m$ -sided polygons". In a series of nested polygons, they are associated inward. The number $n$ inside two triangles is equivalent to $n n$ inside one triangle, which is equivalent to $n n$ raised to the power of $n n$ .

Steinhaus only defined the triangle, the square, and a circle , equivalent to the pentagon defined above.

Steinhaus defined:

Moser's number is the number represented by "2 in a megagon", where a megagon is a polygon with "mega" sides, not to be confused with the megagon, with one million sides.

Alternative notations:

A mega, ②, is already a very large number, since ② = square(square(2)) = square(triangle(triangle(2))) = square(triangle(2²)) = square(triangle(4)) = square(4⁴) = square(256) = triangle(triangle(triangle(...triangle(256)...))) [256 triangles] = triangle(triangle(triangle(...triangle(256²⁵⁶)...))) [255 triangles] ~ triangle(triangle(triangle(...triangle(3.2 × 10⁶¹⁶)...))) [254 triangles] = ...

Using the other notation:

mega = M(2,1,5) = M(256,256,3)

With the function $f(x)=x^{x}$ we have mega = $f^{256}(256)=f^{258}(2)$ where the superscript denotes a functional power, not a numerical power.

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