One Equals Minus One

Paradox
$$ $$ $$ $$

Resolution
This is a falsidical paradox arising from incorrect reasoning about the nature of square roots.

There are two values of $$\sqrt {-1 \times -1}$$.

We have:
 * $$-1 = - \sqrt {-1 \times -1}$$.

We also have:
 * $$1 = + \sqrt {-1 \times -1}$$.

The two are not the same thing.