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The following link indicates the imaginary parts of the non-trivial zeros of the Riemann zeta function $\zeta(s)$ are "discrete" numbers.

New Insight into Proving the Riemann Hypothesis

What is meant by the term "discrete" number with respect to the imaginary part of the non-trivial zeros of $\zeta(s)$?

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  • $\begingroup$ The zeros of $F(s) = \sin(1/s)$ accumulate at $s= 0$ therefore $F$ isn't analytic at $s=0$. $\endgroup$ – reuns Aug 22 '17 at 0:02
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    $\begingroup$ The adjective "discrete" does not apply to the individual zeros, it applies to the set of all zeros. A subset of a topological space inherits a topology, and a topological space is discrete if every subset is open, from which it follows a subset of a topological space is discrete if and only if every one of its points is isolated (is contained in an open subset that does not contain any of the other points). $\endgroup$ – anon Aug 22 '17 at 0:10
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The meaning is that each of the zeros is isolated.

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  • $\begingroup$ as $(s-1)\zeta(s)$ is entire $\endgroup$ – reuns Aug 21 '17 at 23:58

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