Number Theory

    

Simple Proofs that Zeta(n>=2) Is Irrational

Authors: Timothy W. Jones

We prove that partial sums of $\zeta(n)-1=z_n$ are not given by any single decimal in a number base given by a denominator of their terms. This result, applied to all partials, shows that partials are excluded from an ever greater number of rational, possible convergence points. The limit of the partials is $z_n$ and the limit of the exclusions leaves only irrational numbers. Thus $z_n$ is proven to be irrational. Alternative proofs of this same type are given.

Comments: 13 Pages. A clarifying table is added per the comments of a reviewer. Counterexamples are explained.

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Submission history

[v1] 2018-01-12 09:11:07
[v2] 2018-01-13 09:51:26
[v3] 2018-01-14 03:44:54
[v4] 2018-01-15 09:33:09
[v5] 2018-01-18 15:58:09
[v6] 2018-02-13 07:03:38
[v7] 2019-02-26 05:15:02
[v8] 2019-03-12 09:37:10
[v9] 2019-05-12 04:58:17
[vA] 2019-05-22 13:26:22
[vB] 2019-05-25 04:56:21
[vC] 2019-06-04 05:54:05
[vD] 2019-06-06 07:02:55
[vE] 2019-08-15 07:10:00
[vF] 2019-09-28 10:49:52
[vG] 2020-05-17 07:01:41
[vH] 2020-09-07 04:36:09
[vI] 2020-09-10 07:55:22

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