Negative of Real Zero equals Zero

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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

$\blacksquare$


Sources