In mathematics, integers are whole numbers (natural numbers, their negatives and zero).[1] Integers can also be shown on a number line like this:

[math]\displaystyle{ {...-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]\displaystyle{ {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]\displaystyle{ \mathbf{Z} }[/math] or [math]\displaystyle{ \mathbb{Z} }[/math] is the name of the set of integers, and [math]\displaystyle{ \mathbb{Z}_+\! }[/math] is the set of positive integers.[2][3] ([math]\displaystyle{ \mathbf{Z} }[/math], +, 0) is an abelian group.

The number of integers is infinite. The cardinal number of [math]\displaystyle{ \mathbf{Z} }[/math] is [math]\displaystyle{ \aleph_0 }[/math]. The ordinal number of [math]\displaystyle{ \mathbf{Z} }[/math] is [math]\displaystyle{ ^*\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."

Integer Media


  1. Negative numbers have a minus (−) in front of the number. Positive numbers have no sign or a plus (+) sign in front. Zero usually has no sign.
  2. "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-11.
  3. Weisstein, Eric W. "Integer". Retrieved 2020-08-11.