I am attempting to work on the following proof:
If $E$ is an infinite subset of a compact set $K$, then $E$ has a limit point in $K$.
I know that that this proof has been answered here already, but I am more interested in understanding the statement itself. I am just struggling to comprehend what $E$ is in this question... an infinite subset of a compact set. For some reason, I just cannot visualize this. If anyone out there is able to help me see through the fog, or even provide a specific example for me to think about, I would greatly appreciate it.