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>

See also

• algebraic numbers
• abstract algebra