Integer
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.
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 | <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> |