Number Theory

    

Proving Zeta (n>=2) Is Irrational Using Decimal Sets

Authors: Timothy W. Jones

We prove that partial sums of Zeta(n)-1=zn are not given by any single decimal in a number base given by a denominator of their terms. These sets of single decimals we call decimal sets. This result, applied to all partials, shows that partials are excluded from an ever greater number of rational, possible convergence points, elements of these decimal sets. The limit of the partials is zn and the limit of the exclusions leaves only irrational numbers. Thus zn is proven to be irrational.

Comments: 12 Pages.

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[v1] 2020-12-30 12:29:45

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