Number Theory

    

Equipotency of E# with FGH_w

Authors: Sbiis Saibian

The goal in this article is to demonstrate that E# is indeed on the order of ω. Formally this means that for every member of FGH_ω there is a function in E# with at least the same growth rate, and that f_w(n) the smallest member of FGH which eventually dominates over all functions within E#. It will be demonstrated that a certain family of functions of order-type "w" in E# dominates over corresponding members in FGH_w, thus showing that for every function in FGH_w there is a function in E# which grows at least as fast. Then it will be shown how f_w(n) diagonalizes over this family of functions and must eventually dominate every member of this family.

Comments: 21 Pages.

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Submission history

[v1] 2015-03-27 19:39:02

Unique-IP document downloads: 266 times

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