Negative of Real Zero equals Zero

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

  • 2000: James R. Munkres: Topology (2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 4$: The Integers and the Real Numbers: Exercise $1 \ \text{(c)}$
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