Real Number Line is Second-Countable

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

Then $\left({\R, \tau_d}\right)$ is second-countable.

Proof
From Countable Basis of Real Number Space we have that $\left({\R, \tau_d}\right)$ has a countable basis.

The result follows directly from the definition of a second-countable space.