# Bounded sequence implies convergent subsequence

1. Sep 19, 2007

### Scousergirl

How can you deduce that nad bounded sequence in R has a convergent subsequence?

2. Sep 19, 2007

### morphism

This is the Bolzano–Weierstrass theorem. Any decent calculus or analysis textbook should have a proof of it. Or search online. Or use this hint: Prove that a bounded sequence of real numbers has a monotone subsequence.