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.

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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: 66 times

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