Integer

2017-03-14T08:49:10Z

2405:204:3188:CC5:0:0:E0A:8B0: /* Notes */

'''Integers''' are the [[natural numbers]] and their negatives.<ref>Negative numbers have a [[:wikt:minus|minus]] (−) in front of the number. Positive numbers have no sign or a [[:wikt:plus|plus]] (+) sign in front. Zero usually has no sign.</ref>

These are some of the integers:

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

Zero is also an integer but it is not positive nor negative. "Integer" is another word for "whole". An integer is a [[rational number]] with no "fraction", or part. An integer is a [[decimal]] number with all zeros after the [[decimal separator]]. (For example, the integer 17 is the same as the decimal 17.0 or 17.0000.)

An integer has a next smaller number and a next larger number. There is no smallest integer. There is no largest integer. Each integer is either larger than, equal to, or smaller than any integer. [[Consecutive integer]]s are integers that come after each other, like <math>{3, 4, 5, 6.}\,\!</math>

The sum of integers is an integer. The difference between integers is an integer. The product of integers is an integer. (For example, (12 + 2345 x (67 - 8) ) x 9 is an integer.) An integer divided by an integer is sometimes not an integer. (For example, 123 / 45 is not an integer.)

<math>\mathbf{Z}</math> or <math>\mathbb{Z}</math> is the name of the [[set]] of 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 language]]s, like [[C (programming language)|C]], there are types called "int" or "integer."
Integers can also be shown on a number line

== Notes ==
<references/>

{{Math-stub}}

[[Category:Number theory]]
[[Category:Integers| ]]

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Integer