Can someone explain to me what a compact set is?

Question

anonymous · Answer

A compact space is a mathematical space in which any infinite sequence of points sampled from the space must eventually get arbitrarily close to some point of the space. There are several different notions of compactness that are equivalent in good cases. The version I just described is known as sequential compactness.

fellowroot · Answer

Could you possibly give an example of a compact set vs a non compact set. Thanks.

anonymous · Answer

Compact Set: A set S of real numbers is called compact if every sequence in S has a sub-sequence that converges to an element again contained in S.
Perfect Set: A set P is called perfect, if P^1=P  , where P^1 is the derived set of P.
I hope this helps.