I want to prove $S$ is dense in a metric space iff the intersection of $S$ with any open ball in $X$ is non-empty. I have show the first part assuming S is dense in X but I am having trouble going the other way around. I am struggling to construct a sequence in S that goes to an arbitrary $x \in X$. Any help as to how to go about this would be greatly appreciated.
2026-03-27 04:14:56.1774584896
S is dense equivalency statement
19 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in REAL-ANALYSIS
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