Definition:Even Integer

Definition

Let $n$ be an integer.

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

The first few non-negative even numbers are:

$0, 2, 4, 6, 8, 10, \ldots$

This sequence is A005843 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Euclid's Definition

As Euclid defined it:

An even number is that which is divisible into two equal parts.

(The Elements: Book VII: Definition $6$)

Euclid also went further and distinguished between even numbers which are multiples of $4$ and those which are not:

Even-Times Even

As Euclid defined it:

An even-times even number is that which is measured by an even number according to an even number.

(The Elements: Book VII: Definition $8$)

Even-Times Odd

As Euclid defined it:

An even-times odd number is that which is measured by an even number according to an odd number.

(The Elements: Book VII: Definition $9$)

Also see

• Odd Integer

Sources

• Seth Warner: Modern Algebra (1965): $\S 24$