
Direct Proof
Hi Community,
I am having some trouble with this question:
"Show that the additive inverse, or negative, of an even number is an even number using a direct proof. "
I know it's basically asking me to prove that the inverse of an even number is even. I'm having trouble expressing it in English/ Mathematical operators.
I have:
Let n = 2a, for all !n=2a, n is even
Someone help?
M

The additive inverse of a number x is denoted (x)
All even numbers are defined to be $\displaystyle \{ 2a  a\in\mathbb{Z} \}$
So we have an even number. Let's call it 2a.
Well it's inverse is $\displaystyle (2a)=(1)(2a)=(2a)(1)=2(a(1))=2(a)$, but if $\displaystyle a\in\mathbb{Z}$, then $\displaystyle a\in\mathbb{Z}$, and so $\displaystyle (2a)$ is an even number