# Real numbers/Bolzano Weierstraß/Fact

Bolzano–Weierstrass theorem

Let denote a bounded sequence of real numbers.

Then this sequence has a
subsequence.

Bolzano–Weierstrass theorem

Let ${}{\left(x_{n}\right)}_{n\in \mathbb {N} }$ denote a bounded sequence of real numbers.

Then this sequence has a
subsequence.