Order is Preserved on Positive Reals by Squaring/Proof 3
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Theorem
- $x < y \iff x^2 < y^2$
Proof
From Real Numbers form Ordered Field, the real numbers form an ordered field.
By definition, an ordered field is a totally ordered ring without proper zero divisors.
The result follows from Order of Squares in Totally Ordered Ring without Proper Zero Divisors.
$\blacksquare$