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

\(\ds -0 + 0\) \(=\) \(\ds 0\) Real Number Axiom $\R \text A4$: Inverses for Addition
\(\ds \leadsto \ \ \) \(\ds -0\) \(=\) \(\ds 0\) Real Addition Identity is Zero: Corollary

$\blacksquare$


Sources