Given $X$ metric space and $E$ is any subset of $X$.
If $x$ is a limit point of $E$, for every $\epsilon>0$, prove that neighborhood of x contains infinitely many element
I use the fact that when we have $x$ as a limit point of $E$, we can find a sequence on $E$ that converges to $x$, and because the sequence on $E$ and subset of neighborhood of $x$, we can conclude that neighborhood of $x$ contain infinitely many elements
Does my argument make sense? I hope you can tell me if I'm wrong guys