Product of Negative Real Numbers is Positive
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Theorem
Let $a, b \in \R_{\le 0}$ be negative real numbers.
Then:
- $a \times b \in \R_{\ge 0}$
That is, their product $a \times b$ is a positive real number.
Proof
From Real Numbers form Ring, the set $\R$ of real numbers forms a ring.
The result then follows from Product of Ring Negatives.
$\blacksquare$
Sources
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1.1$. Number Systems