User:Bedelato

Any number is equal to its negative

Assume a and b are real numbers.

We start with:

$b=-a$

From this we can also conclude:

$a=-b$

Square each side:

$(a)^{2}=(-b)^{2}$

A negative times a negative is a positive:

$a^{2}=b^{2}$

Take the square root:

${\sqrt {a^{2}}}={\sqrt {b^{2}}}$

We get:

$a=b$

From our original equation b=-a:

$a=-a$

This plainly shows that any number is equal to its negative.