This article is about the generalization of the basic concept. For the basic concept, see Absolute value. For other uses, see Absolute value (disambiguation).In mathematics, an absolute value is a function which measures the "size" of elements in a field or integral domain.

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  • This article is about the generalization of the basic concept. For the basic concept, see Absolute value. For other uses, see Absolute value (disambiguation).In mathematics, an absolute value is a function which measures the "size" of elements in a field or integral domain. More precisely, if D is an integral domain, then an absolute value is any mapping | x | from D to the real numbers R satisfying: | x | ≥ 0, | x | = 0 if and only if x = 0, | xy | = | x || y |, | x + y | ≤ | x | + | y |.It follows from these axioms that | 1 | = 1 and | −1 | = 1. Furthermore, for any positive integer n,| n | = | 1+1+...(n times) | = | −1−1...(n times) | ≤ n.Note that some authors use the terms valuation, norm, or magnitude instead of "absolute value". However, the word "norm" usually refers to a specific kind of absolute value on a field (and which is also applied to other vector spaces).The classical "absolute value" is one in which, for example, |2|=2. But many other functions fulfill the requirements stated above, for instance the square root of the classical absolute value (but not the square thereof).
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  • This article is about the generalization of the basic concept. For the basic concept, see Absolute value. For other uses, see Absolute value (disambiguation).In mathematics, an absolute value is a function which measures the "size" of elements in a field or integral domain.
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  • Valeur absolue ultramétrique
  • Absolute value (algebra)
  • Valor absoluto (álgebra)
  • Нормирование
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