Difference between revisions of "Integer"

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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>   
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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 10:01, 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:

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

See also