Usual metric on the real line

Example

On the set $\mathbb{R}$ of real numbers, let $$d(x, y) = |x - y|,$$ where $|\cdot|$ is the absolute value. Then $d$ is a metric on $\mathbb{R}$. The triangle inequality for real numbers gives the triangle inequality for $d$.

Remarks

The number $|x - y|$ is the absolute difference of $x$ and $y$. This metric is the case $n = 1$ of the Euclidean metric. The same formula with the modulus gives a metric on the complex numbers.

Explanations

L1 human

The distance between two numbers is the length of the segment between them on the number line. For example, the distance between $-2$ and $3$ is $|-2 - 3| = 5$.