# Integer

## number that can be written without a fractional or decimal component / From Wikipedia, the free encyclopedia

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

${...-4,-3,-2,-1,0,+1,+2,+3,+4,...}\,\!$

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 ${1,2,3,4}$).

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).

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

The number of integers is infinite. The cardinal number of $\mathbf {Z}$ is $\aleph _{0}$. The ordinal number of $\mathbf {Z}$ is $^{*}\omega +\omega$.

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