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Line 1: − + − More precisely, the set of all integers consists of all natural numbers {1, 2, 3, 4, ...}, their negatives {-1, -2, -3, -4, ...} and 0. A formal definition is that it is the only [[integral domain]] whose positive elements are well ordered and in which order is preserved by addition.+ − + − + + + + + Line 11:
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→See also: clean up & uniformity
An '''integer''' is any whole number, positive, negative, or 0. Starting at 1 and going up are the [[counting numbers]] {1, 2, 3, 4, ...}, sometimes called "natural numbers".
An '''integer''' is any number that does not have any fractional or decimal components. Numbers such as 1,2 and -3 are integers, but 2½, √5 are not. The mathematical symbol for this set is <math>\mathbb{Z}</math>. More precisely, the set of all integers consists of all natural numbers {1, 2, 3, 4, ...}, their negatives {-1, -2, -3, -4, ...} and 0. A formal definition is that it is the only [[integral domain]] whose positive elements are well ordered and in which order is preserved by addition. Integers are often colloquially referred to as "whole numbers," though this terminology is not well defined and is often used to refer to only a subset of integers, such as the positive integers.
An integer may be:
* [[even number|even]] (divisible by two)
An integer may be [[even number|even]] (divisible by two) or [[odd number|odd]] (not divisible by two), [[positive number|positive]] (more than [[zero]]) or [[negative number|negative]] (less than zero), [[whole number|whole]] (undivided) or composite (divisible into other integers), and various other classifications, such as [[prime]] (only divisible by itself and one).
* [[odd number|odd]] (not divisible by two)
* [[positive number|positive]] (more than [[zero]])
* [[negative number|negative]] (less than zero)
* [[whole number|whole]] (undivided)
* [[composite]] (divisible into other integers) or [[prime]] (only divisible by itself and one)
Every integer larger than 1 has a unique [[prime factorization]].
Every integer larger than 1 has a unique [[prime factorization]].
Likewise, the following numbers are not integers: 5/10, the square root of -9, 8.75, and [[pi]].
Likewise, the following numbers are not integers: 5/10, the square root of -9, 8.75, and [[pi]].
See also:
Some [[subset]]s of the integers are often used. They have their own symbols:
{| class="wikitable"
|-
! set
! name
! symbol
|-
| ..., -2, -1, 0, 1, 2, ...
| integers
| <math>\mathbb{Z}</math>
|-
| 1, 2, 3, 4, ...
| positive integers
| <math>\mathbb{Z}^+</math>
|-
| 0, 1, 2, 3, 4, ...
| nonnegative integers
| <math>\mathbb{Z}^*</math>
|-
| 0, -1, -2, -3, -4, ...
| nonpositive integers
|
|-
| -1, -2, -3, -4, ...
| negative integers
| <math>\mathbb{Z}^-</math>
|}
==See also==
*[[algebraic numbers]]
*[[algebraic numbers]]
*[[abstract algebra]]
*[[abstract algebra]]
[[category:mathematics]]
[[Category:Mathematics]]