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:

$Integer$

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

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

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.

In programming

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

Somewhat confusingly ^[4] , integers don't always correspond to exactly one type in a programming language, such as:

char, short, int, long, long long in C
int, bignum in Python

All seven of the above types are integers.

"Unsigned" integers are not allowed to have a negative sign, such as ${0,+1,+2,+3,...}$

"Signed" integers are allowed to have a negative sign (or positive sign or no sign), such as ${-3,-2,-1,0,+1,+2,+3,...}$

Notes

↑ 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, but in rare cases such as One's Complement and Sign-magnitude, both $+0$ and $-0$ co-exist.
↑ "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-11.
↑ Weisstein, Eric W. "Integer". mathworld.wolfram.com. Retrieved 2020-08-11.
↑ Multiple types exist for integers due to the biggest and smallest representable numbers varying among the types.

v t e Number systems
Commonly used systems	Natural numbers ( $\mathbb {N}$ ) Integers ( $\mathbb {Z}$ ) Rational numbers ( $\mathbb {Q}$ ) Real numbers ( $\mathbb {R}$ ) Complex numbers ( $\mathbb {C}$ )
Hypercomplex numbers	Quaternions ( $\mathbb {H}$ ) Octonions ( $\mathbb {O}$ ) Sedenions ( $\mathbb {S}$ ) Trigintaduonions ( $\mathbb {T}$ )

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Integer

Jumat, 2026-03-13 13:30:42

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

Integer

In programming

Notes

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