Basic Analysis I — Real Analysis · Problem 7.3.7

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · sequences-and-convergence

Problem

A set

S \subset X

is said to be dense in

X

X \subset \overline{S}

or in other words if for every

p \in X

, there exists a sequence

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

S

that converges to

p

. Prove that

\mathbb{R}^n

contains a countable dense subset.