User:Bedelato

Any number is equal to its negative

left

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.