Definition:Even Integer

Definition
Let $n \in \Z$ be an integer.

Then $n$ is even it has $2$ as a divisor.

That is, $n$ is even it is of the form $n = 2 r$ where $r \in \Z$ is an integer.

The set of even integers can be denoted $2 \Z$.

The first few non-negative even integers are:
 * $0, 2, 4, 6, 8, 10, \ldots$

Euclid's Definition


Euclid went further and categorised even numbers according to:
 * whether they are multiples of $4$

and:
 * whether they have an odd divisor:

Also see

 * Definition:Odd Integer