Integer

Pronunciation: /ˈɪn tɪ dʒər/ Explain

An integer is a whole number having no decimal part. An integer can be a positive whole number, a negative whole number, or zero. Examples of integers are 24, -142, and 0. The symbol for the set of natural numbers is a double struck capital N: &0x2115;. The definition of the set of integer in set notation is &0x2115;={..., -3, -2, -1, 0, 1, 2, 3, ..}.

In math, we can represent integers in ways that may not look like integers at first. For example, the fraction 8/4 can be reduced to 2, and so is an integer, even if it is represented by an improper fraction.

Another example is 5.00. While it is represented using decimal notation, it has a decimal part of 0, which is the same as no decimal part. However, in most computer based systems, 5.00 would be stored as a decimal number, not as an integer.

Here are some examples of numbers that are not integers: 5.2, 12/7 (can not be reduced to a single whole number), p (has been proved to be irrational), and 0.3 (contains non-zero digits after the decimal point).

Properties of Integers

The set of integers is associative with respect to addition, subtraction, multiplication and division.The set of integers is commutative with respect to addition and multiplication. The set of integers is not commutative with respect to subtraction or division.
PropertyDescription
Associativity
Commutativity
Additive identityThe additive identity for integers is 0.
Multiplicative identityThe multiplicative identity for integers is 1.
ClosureThe set of integers is closed with respect to addition, subtraction and multiplication. The set of integers is not closed with respect to division.
DiscreteThe set of integers is a discrete (not continuous) set.
CardinalityThe cardinality of the set of integers is 0.
Table 1: Properties of the integers.

Check Mark Understanding Check

Decide if each number represents an integer. Then click either 'integer' or 'not an integer'.

NumberIs an integer?
15no answer Integer
no answer Not an integer
-6.4 no answer Integer
no answer Not an integer
5/7 no answer Integer
no answer Not an integer
-2.0000 no answer Integer
no answer Not an integer
square root of 2no answer Integer
no answer Not an integer
8/2 no answer Integer
no answer Not an integer
p no answer Integer
no answer Not an integer
square root of 4 no answer Integer
no answer Not an integer

References

  1. Jones, Burton. Elementary Concepts of Mathematics. pp 86-91. www.archive.org. MacMillan and Company. 1947. Last Accessed 8/6/2018. http://www.archive.org/stream/elementaryconcep029487mbp#page/n108/mode/1up/search/integer. Buy the book
  2. Fish, Daniel W.. Robinson's Practical Arithmetic. pg 85. www.archive.org. Ivison, Blakeman, Taylor & Co.. 1881. Last Accessed 8/6/2018. http://www.archive.org/stream/numberstheory00robirich#page/84/mode/1up.
  3. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 57-63. Thomson, Brooks/Cole. 2005. Buy the book

Cite this article as:

McAdams, David E. Integer. 8/7/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/integer.html.

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Revision History

8/6/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
2/17/2010: Added "References". (McAdams, David E.)
11/25/2008: Changed equations to images. (McAdams, David E.)
8/11/2008: Added 'More Information' and 'Understanding Check'. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

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