Definition:Odd Integer/Definition 1

Definition

An integer $n \in \Z$ is odd if and only if it is not divisible by $2$.

That is, if and only if it is not even.

Euclid's Definition

In the words of Euclid:

An odd number is that which is not divisible into two equal parts, or that which differs by an unit from an even number.

Sequence of Odd Integers

The first few non-negative odd integers are:

$1, 3, 5, 7, 9, 11, \ldots$