Absolute Value

Overview

Let $x\in \mathbb{R}$. The absolute value of $x$, denoted $|x|$, is defined as

Triangle Inequality

Let $x,y\in \mathbb{R}$. Then the triangle inequality of $\mathbb{R}$ states

Geometrically speaking, any side of a triangle is less than or equal to the sum of the other two sides.

Reverse Triangle Inequality

Let $x,y\in \mathbb{R}$. Then the reverse triangle inequality of $\mathbb{R}$ states

Geometrically speaking, any side of a triangle is greater than or equal to the difference of the other two sides.