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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 number that does not have any fractional or decimal components. Numbers such as 1,2 and -3 are integers, but 2½, √5 are not. The mathematical symbol for this set is <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. Integers are often colloquially referred to as "whole numbers," though this terminology is not well defined and is often used to refer to only a subset of integers, such as the positive integers.

 

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:

An integer may be:

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]].  

==See also==

==See also==

*[[abstract algebra]]

*[[abstract algebra]]

[[category:mathematics]]

[[Category:Mathematics]]