Number Theory

   

Gamma is Irrational

Authors: Timothy W. Jones

We introduce an unaccustomed number system, H±, and show how it can be used to prove gamma is irrational. This number system consists of plus and minus multiplies of the terms of the harmonic series. Using some properties of ln, this system can depict the harmonic series and lim as n goes to infinity of ln n at the same time, giving gamma as an infinite decimal. The harmonic series converges to infinity so negative terms are forced. As all rationals can be given in H± without negative terms, it follows that must be irrational.

Comments: 4 Pages.

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[v1] 2018-08-21 08:06:10

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