Real Number Line is Second-Countable

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

Then $\struct {\R, \tau_d}$ is second-countable.

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

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