Proving Even Number Additive Inverse is Even

[XodoX]

Homework Statement

How do I show that the additive inverse, or negative, of an even number is an even number ( direct proof) ?

Homework Equations

The Attempt at a Solution

I have no idea. Anybody?

 

[hunt_mat]

Really? Let $$a=2n$$ be an even number then the additive inverse $$b$$ is defined by $$a+b=0$$, so $$b=-a=-2n$$, and so...

 

[tiny-tim]

alternatively, start "an even number is a + a, so …"

 

[XodoX]

Thanks! Makes sense now.