Integer

An integer is any number evenly divisible by 1. The mathematical symbol for this set is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{Z}} . Starting at 1 and going up are the counting numbers {1, 2, 3, 4, ...}, sometimes called "natural numbers" - symbolized by $\mathbb {N}$ or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{Z}^+}

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	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{Z}}
1, 2, 3, 4, ...	positive integers	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{Z}^+}
0, 1, 2, 3, 4, ...	nonnegative integers	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{Z}^*}
0, -1, -2, -3, -4, ...	nonpositive integers
-1, -2, -3, -4, ...	negative integers	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{Z}^-}

See also

• algebraic numbers
• abstract algebra