Integer (nonfiction): Difference between revisions
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An '''integer''' (from the Latin ''integer'' meaning "whole") is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 1⁄2, and √2 are not. | [[File:Zahlen_symbol.svg|thumb|The Blackboard Bold Z symbol represents the set of integer numbers. The symbol derives from the German word ''Zahlen'' ([ˈtsaːlən], "numbers").]]An '''integer''' (from the Latin ''integer'' meaning "whole") is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 1⁄2, and √2 are not. | ||
The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, …), also called whole numbers or counting numbers, and their additive inverses (the '''negative integers''', i.e., −1, −2, −3, …). This is often denoted by a boldface Z ("Z") or blackboard bold Z (Unicode U+2124 ℤ) standing for the German word ''Zahlen'' ([ˈtsaːlən], "numbers"). | The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, …), also called whole numbers or counting numbers, and their additive inverses (the '''negative integers''', i.e., −1, −2, −3, …). This is often denoted by a boldface Z ("Z") or blackboard bold Z (Unicode U+2124 ℤ) standing for the German word ''Zahlen'' ([ˈtsaːlən], "numbers"). | ||
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== Nonfiction cross-reference == | == Nonfiction cross-reference == | ||
* [[Irrational number (nonfiction)]] | |||
* [[Mathematics (nonfiction)]] | * [[Mathematics (nonfiction)]] | ||
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* [https://en.wikipedia.org/wiki/Integer Integer] @ Wikipedia | * [https://en.wikipedia.org/wiki/Integer Integer] @ Wikipedia | ||
[[Category:Nonfiction (nonfiction)]] | [[Category:Nonfiction (nonfiction)]] | ||
[[Category:Mathematics (nonfiction)]] | [[Category:Mathematics (nonfiction)]] | ||
Revision as of 12:38, 14 November 2017
An integer (from the Latin integer meaning "whole") is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 1⁄2, and √2 are not.
The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, …), also called whole numbers or counting numbers, and their additive inverses (the negative integers, i.e., −1, −2, −3, …). This is often denoted by a boldface Z ("Z") or blackboard bold Z (Unicode U+2124 ℤ) standing for the German word Zahlen ([ˈtsaːlən], "numbers").
ℤ is a subset of the sets of rational numbers ℚ, in turn a subset of the real numbers ℝ. Like the natural numbers, ℤ is countably infinite.
The integers form the smallest group and the smallest ring containing the natural numbers.
In algebraic number theory, the integers are sometimes called rational integers to distinguish them from the more general algebraic integers. The (rational) integers are the algebraic integers that are also rational numbers.
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External links:
- Integer @ Wikipedia