Number Theory


Visualizing Zeta(n>1) and Proving Its Irrationality

Authors: Timothy W. Jones

A number system is developed to visualize the terms and partials of zeta(n>1). This number system consists of radii that generate sectors. The sectors have areas corresponing to all rational numbers and can be added via a tail to head vector addition. Dots on the circles give an un-ambiguous cross reference to decimal systems in all bases. We show, in the proof section of this paper, first that all partials require decimal bases greater than the last denominator used in the partial, then that this can be used to make a sequence of nested intervals with rational endpoints. Using Cantor's Nested Interval theorem this gives the convergence point of zeta series and disallows rational values, thus proving the irrationality of zeta(n>1).

Comments: 17 Pages. Replaces use of Cantor's Diagonal Method with a set topological proof.

Download: PDF

Submission history

[v1] 2017-10-12 05:04:05
[v2] 2017-10-21 05:31:18
[v3] 2017-11-02 10:23:05
[v4] 2017-12-21 08:13:33
[v5] 2017-12-30 12:01:50

Unique-IP document downloads: 70 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus