Real Number Line is Separable/Proof 2

Theorem
Let $\left({\R, \tau_d}\right)$ be the real number line under the Euclidean metric considered as a topological space.

Then $\left({\R, \tau_d}\right)$ is separable.

Proof

 * Real Number Space is Second-Countable
 * Second-Countable Space is Separable