Multiplication by Negative Real Number/Corollary

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Corollary to Multiplication by Negative Real Number

$\forall x \in \R: \paren {-1} \times x = -x$


Proof

\(\ds \paren {-1} \times x\) \(=\) \(\ds -\paren {1 \times x}\) Multiplication by Negative Real Number
\(\ds \) \(=\) \(\ds -x\) Real Number Axiom $\R \text M3$: Identity Element for Multiplication

$\blacksquare$


Sources