Basic Analysis I — Real Analysis · Problem 2.3.3

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · limit-superior-limit-inferior

Problem

Finish the proof of Proposition 2.3.6. That is, suppose

\{x_n\}_{n=1}^\infty

is a bounded sequence and

\{x_{n_k}\}_{k=1}^\infty

is a subsequence. Prove

\liminf_{n\to\infty} x_n \leq \liminf_{k\to\infty} x_{n_k}