I am trying to find an example of a metric on $\mathbb N$ with no isolated points.Is it possible to define such a metric?
2026-04-02 18:39:18.1775155158
A metric on $\mathbb N$ with no isolated points.
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Let $(r_n)$ be an arrangement of rational numbers in a sequence. Define $d(n,m)=|r_n-r_m|$. This gives a metric on $\mathbb N$ with no isolated points.