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subsets of the integers, symbols
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 whole number, positive, negative, or 0. The mathematical symbol for this set is <math>\mathbb{Z}</math>. Starting at 1 and going up are the [[counting numbers]] {1, 2, 3, 4, ...}, sometimes called "natural numbers" - symbolized by <math>\mathbb{N}</math> or <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.
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.
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]].
Some [[subsets]] 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==
==See also==