# Real Number Ordering is Compatible with Multiplication

## 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

$\forall a, b, c \in \R: a < b \land c < 0 \implies a c > b c$