# Using the order axioms of $\mathbb{R}$ to prove the semi-definite positivity property for the absolute value?

How can I use the order axioms of $$\mathbb{R}$$ to prove the semi-definite positivity property for the absolute value:

For all $$x \in \mathbb{R}, |x|\geq0$$ and $$|x|=0$$ if and only if $$x=0$$?

• Hi Jake! What have you tried so far? – user458276 Feb 5 at 16:12
• @user458276 I have tried proving by contradiction. So, suppose $|x|\geq0$ and $|x|=0$ and $x\neq0$. Obviously, we have a contradiction because $x$ cannot both be 0 and not 0. I just don't see the motivation behind using the order axioms of the reals. – Jake Feb 5 at 16:15