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