Baire Category Theorem/Corollary

Corollary to Baire Category Theorem
The real number line $\R$ with the usual (Euclidean) metric is non-meager.

Proof
From Real Number Line is Complete Metric Space, $\R$ is a complete metric space.

From the Baire Category Theorem, a complete metric space is a Baire space.

The result follows from Baire Space is Non-Meager.