# sequential compactness

#### 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.

#### Plato

MHF Helper
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 $$\displaystyle E$$ with no accumulation point in $$\displaystyle X$$?