# Difference between revisions of "Integer"

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− | An '''integer''' is any | + | An '''integer''' is any number evenly divisible by 1. 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. |

## Revision as of 09:01, 22 February 2013

An **integer** is any number evenly divisible by 1. The mathematical symbol for this set is . Starting at 1 and going up are the counting numbers {1, 2, 3, 4, ...}, sometimes called "natural numbers" - symbolized by or

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.

An integer may be:

- even (divisible by two)
- odd (not divisible by two)
- positive (more than zero)
- negative (less than zero)
- 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.

Some examples of integers: 1, 10/5, 98058493, -87, -3/3, both square roots of 9, and 0.

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:

set | name | symbol |
---|---|---|

..., -2, -1, 0, 1, 2, ... | integers | |

1, 2, 3, 4, ... | positive integers | |

0, 1, 2, 3, 4, ... | nonnegative integers | |

0, -1, -2, -3, -4, ... | nonpositive integers | |

-1, -2, -3, -4, ... | negative integers |