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

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 $\zeta(s)$?

• The zeros of $F(s) = \sin(1/s)$ accumulate at $s= 0$ therefore $F$ isn't analytic at $s=0$. – reuns Aug 22 '17 at 0:02
• 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). – anon Aug 22 '17 at 0:10

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