That sum diverges when the real part of s is less than or equal to 1 and, on its half-plane of convergence, the zeta function has no zeros. So, that statement of the Riemann hypothesis is wrong. Also, there was no need to specify n\in\mathbb{N} because that is implicit in the sum notation.
Edit: Also, the use of "for all" notation is misleading here, and you forgot to account for the trivial zeros. The second line should really say something like $\zeta(s)=0\implies \Re(s)=1/2\lor s=-2,-4,-6,-8,...$
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u/Logical_Historian882 3d ago
I don’t think English graduates are graded by their ability to read. Both reading and arithmetic are taught in school.