Number Theory


Using Cantor's Diagonal Method to Show Zeta(2) is Irrational

Authors: Timothy W. Jones

We look at some of the details of Cantor's Diagonal Method and argue that the swap function given does not have to exclude 9 and 0, base 10. We also puzzle out why the convergence of the constructed number, its value, is of no concern. We next review general properties of decimals and prove the existence of an irrational number with a modified version of Cantor's diagonal method. Finally, we show, with yet another modification of the method, that Zeta(2) is irrational.

Comments: 10 Pages. Some reviewers pointed out an error. It's fixed. Clarifications.

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Submission history

[v1] 2018-10-20 11:17:11
[v2] 2018-10-23 12:29:15
[v3] 2018-10-28 12:02:04
[v4] 2018-11-01 08:29:23
[v5] 2018-11-09 08:01:59
[v6] 2018-11-11 12:07:54
[v7] 2018-11-29 10:43:21

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