Real Number Line is Separable/Proof 2

Theorem

Let $\struct {\R, \tau_d}$ be the real number line with the usual (Euclidean) topology.

Then $\struct {\R, \tau_d}$ is separable.

Proof

Follows from:

Real Number Line is Second-Countable

Second-Countable Space is Separable

$\blacksquare$