Integer

In mathematics, integers are whole numbers (natural numbers, their negatives, and zero). Integers can also be shown on a number line like this:

<math>{...-4, -3, -2, -1, 0, +1, +2, +3, +4,...}\,\!</math>

In particular, zero or 0 is an integer that is neither positive nor negative. An integer is a whole number with no fractional or decimal part.

Integers have no smallest or largest value because for any given integer, there is always a larger and smaller integer. Any integer is either greater than or smaller than any other integer. Consecutive integers are integers that come after each other (as in <math>{1, 2, 3, 4}</math>).

The sum, difference and product of integers is always an integer.(for example, (12 + 2345 × (67 - 8)) × 9 is an integer). An integer divided by an integer is sometimes not an integer (for example, 1 ÷ 2 = 0.5).

<math>\mathbf{Z}</math> or <math>\mathbb{Z}</math> is the name of the set of integers, and <math>\mathbb{Z}_+\!</math> is the set of positive integers. (<math>\mathbf{Z}</math>, +, 0) is an abelian group.

The number of integers is infinite. The cardinal number of <math>\mathbf{Z}</math> is <math>\aleph_0</math>. The ordinal number of <math>\mathbf{Z}</math> is <math>^*\omega + \omega</math>.

To sum up, an integer is a whole number that has no decimals.

In programming

In some programming languages, like C, there are types called "int" or "integer."