Basic Analysis I — Real Analysis · Problem 2.1.18

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · sequences-and-limits

Problem

(Easy) Let

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

be a sequence and

x \in \mathbb{R}

. Suppose for every

\epsilon > 0

, there is an

M

such that

|x_n - x| \leq \epsilon

for all

n \geq M

. Show that

\lim_{n\to\infty} x_n = x