Definition:Odd Integer

Definition
Let $n \in \Z$, i.e. let $n$ be an integer.

Definition 1
Then $n$ is odd it is not divisible by $2$.

That is, it is not even.

Definition 2
More precisely, $n$ is odd if there exists some integer $x$, such that $n = 2 x + 1$.

Also see

 * Definition:Even Integer