Prove that a even number + odd number = odd number
Let $x$ be the even number, let $y$ be the odd number.
From the definition of odd numbers, $y + 1$ is even.
Let:
$$x + y = z$$
Suppose $z$ is even.
$$x + y = z$$
It follows that:
$$x = x + y – y = z – y$$
But I cant think of any other contradiction here. The issue is with the assumption I suppose. Any help is appreciated!
Best Answer
An even number $n$ can always be written as $2k$. An odd number $m$ can always be written as $2h+1$.
Hence $n+m=2k+2h+1=2(h+k)+1$ which is odd.