Integer

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

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

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

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).

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

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

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

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". mathworld.wolfram.com. Retrieved 2020-08-11.