Absolute Value is Bounded Below by Zero

Theorem
Let $$x$$ be a real number, i.e. that $$x \in \mathbb{R}$$.

Then the absolute value $$\left|{x}\right|$$ of $$x$$ is bounded below by $$0$$.

Proof

 * Let $$x \ge 0$$.

Then $$\left|{x}\right| = x \ge 0$$.


 * Let $$x < 0$$.

Then $$\left|{x}\right| = -x > 0$$.

The result follows.