Negative of Sum of Real Numbers/Corollary
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Theorem
- $\forall x, y \in \R: -\paren {x - y} = -x + y$
Proof
\(\ds -\paren {x - y}\) | \(=\) | \(\ds -\paren {x + \paren {-y} }\) | Definition of Real Subtraction | |||||||||||
\(\ds \) | \(=\) | \(\ds -x - \paren {-y}\) | Negative of Sum of Real Numbers | |||||||||||
\(\ds \) | \(=\) | \(\ds -x + \paren {-\paren {-y} }\) | Definition of Real Subtraction | |||||||||||
\(\ds \) | \(=\) | \(\ds -x + y\) | Negative of Negative Real Number |
$\blacksquare$
Sources
- 2000: James R. Munkres: Topology (2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 4$: The Integers and the Real Numbers: Exercise $1 \ \text{(h)}$