# Math Help - sequential compactness

1. ## sequential compactness

How do you prove the following theorem?
If X is a metric space and E a subset of X is compact, then E is sequentially compact.

2. Originally Posted by Alex314
How do you prove the following theorem?
If X is a metric space and E a subset of X is compact, then E is sequentially compact.
Is it possible that there is an infinite subset of $E$ with no accumulation point in $X$?