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Math and science::Analysis::Tao::06. Limits of sequences

Bolzano-Weierstrass theorem

Let \( (a_n)_{n=0}^{\infty} \) be a bounded sequence (i.e. there exists a real number \( M > 0 \) such that \( |a_k| \le M \text{ for all } k \in N \)). Then there is at least one [...] which [...].