Real Number Line is Metric Space

Theorem
Let $$\mathbb{R}$$ be the set of all real numbers.

Let $$d: \mathbb{R} \times \mathbb{R} \to \mathbb{R}$$ be defined as:

$$d \left({x_1, x_2}\right) = \left|{x_1 - x_2}\right|$$, where $$\left|{x}\right|$$ is the absolute value of $$x$$.

Then $$d$$ is a metric on $$\mathbb{R}$$ and so $$\left\{{\mathbb{R}, d}\right\}$$ is a metric space.

Proof
From the definition of absolute value:

$$\left|{x_1 - x_2}\right| = \sqrt {\left({x_1 - x_2}\right)^2}$$.

It is clear that this is the same as the euclidean metric, which is shown in Euclidean Metric is a Metric to be a metric.

Thus the real number line is a 1-dimensional Euclidean space.