Êtes-vous un étudiant de l'EPFL à la recherche d'un projet de semestre?
Travaillez avec nous sur des projets en science des données et en visualisation, et déployez votre projet sous forme d'application sur Graph Search.
Concept
Steinhaus–Moser notation
Résumé
In mathematics, Steinhaus–Moser notation is a notation for expressing certain large numbers. It is an extension (devised by Leo Moser) of Hugo Steinhaus's polygon notation.
a number n in a triangle means nn.
a number n in a square is equivalent to "the number n inside n triangles, which are all nested."
a number n in a pentagon is equivalent with "the number n inside n squares, which are all nested."
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 nn inside one triangle, which is equivalent to nn raised to the power of nn.
Steinhaus defined only the triangle, the square, and the circle , which is equivalent to the pentagon defined above.
Steinhaus defined:
mega is the number equivalent to 2 in a circle:
megiston is the number equivalent to 10 in a circle: 10
Moser's number is the number represented by "2 in a megagon". Megagon is here the name of a polygon with "mega" sides (not to be confused with the polygon with one million sides).
Alternative notations:
use the functions square(x) and triangle(x)
let M(n, m, p) be the number represented by the number n in m nested p-sided polygons; then the rules are:
and
mega =
megiston =
moser =
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(3.2317 × 10616)...))) [255 triangles]
Using the other notation:
mega = M(2,1,5) = M(256,256,3)
With the function we have mega = where the superscript denotes a functional power, not a numerical power.
We have (note the convention that powers are evaluated from right to left):
M(256,2,3) =
M(256,3,3) = ≈
Similarly:
M(256,4,3) ≈
M(256,5,3) ≈
M(256,6,3) ≈
etc.
Source officielle
À propos de ce résultat
Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.