(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let X be an infinite set. For p,q [tex]\in[/tex] X define:

d(p,q) = {1 if p [tex]\neq[/tex] q; 0 if p = q

Suppose E is a finite subset of X, find all limit points of E.

2. Relevant equations

definition: a point p is a limit point of E if every neighborhood of p contains a point q [tex]\neq[/tex] p s.t. q[tex]\in[/tex]E

3. The attempt at a solution

My thoughts were that there are no limit points for any subset of X because for any point p, B(p, 1/n) is empty, [tex]\forall[/tex]n[tex]\in[/tex]N. Therefore, for any point p, there exists at least one neighborhood that contains no points q [tex]\in[/tex] E.

I feel that this is true, but have I made any incorrect assumptions??

Thanks a lot for any feedback.

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# Homework Help: Finite subset of a metric space

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