We can think of the absolute value of a number as its distance from 0. So, the absolute value of a, which is denoted by is always greater than 0. In this post, we are going to prove that for all real numbers a, |-a| = |a|.

There are two possible cases: and $latex b < 0$. (i) For $latex a \geq 0$, $latex since - a \leq 0$ $latex |-a| = -(-a) = a$ (since a is negative, we negate it to make it positive) $latex |a| = a$ (ii) For $latex a < 0$, since $latex - a > 0$,

= (since a is negative, we negate it to make it positive)

By (i) and (ii), for any real number a,

.