Number Theory


Extending an Irrationality Proof of Sondow: from e to Zeta(n)

Authors: Timothy W. Jones

We modify Sondow's geometric proof of the irrationality of e. The modification uses sector areas on circles, rather than closed intervals. Using this circular version of Sondow's proof, we see a way to understand the irrationality of a series. We evolve the idea of proving all possible rational value convergence points of a series are excluded because all partials are not expressible as fractions with the denominators of their terms. If such fractions cover the rationals, then the series should be irrational. Both the irrationality of e and that of zeta(n>=2) are proven using these criteria: the terms cover the rationals and the partials escape the terms.

Comments: 16 Pages. A new section that shows with greater clarity the extension of Sondow has been added.

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Submission history

[v1] 2019-03-27 07:27:20
[v2] 2019-04-05 09:59:59
[v3] 2019-04-15 05:15:24
[v4] 2019-04-17 03:51:24

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