# Negative of Real Zero equals Zero

## Theorem

Let $0$ denote the identity for addition in the real numbers $\R$.

Then:

$-0 = 0$

## Proof

 $\displaystyle -0 + 0$ $=$ $\displaystyle 0$ Real Number Axioms: $\R A 4$ $\displaystyle \leadsto \ \$ $\displaystyle -0$ $=$ $\displaystyle 0$ Real Addition Identity is Zero: Corollary

$\blacksquare$