Real Number Ordering is Compatible with Multiplication
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Theorem
Let $\R$ denote the set of real numbers.
Then:
Positive Factor
- $\forall a, b, c \in \R: a < b \land c > 0 \implies a c < b c$
Negative Factor
- $\forall a, b, c \in \R: a < b \land c < 0 \implies a c > b c$