Absolute Value of Product/Proof 4

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Theorem

Let $x, y \in \R$ be real numbers.


Then:

$\size {x y} = \size x \size y$

where $\size x$ denotes the absolute value of $x$.


Thus the absolute value function is completely multiplicative.


Proof

Follows directly from:

Real Numbers form Ordered Integral Domain
Product of Absolute Values on Ordered Integral Domain.

$\blacksquare$