Editing Absolute value (section)

{{Short description|Distance from zero to a number}}
{{about|the absolute value of real and complex numbers|a generalization of the concept|Absolute value (algebra)|other uses}}
{{Use dmy dates|date=December 2020}}
[[Image:Absolute value.svg|thumb|The [[graph of a function|graph]] of the absolute value function for real numbers]]
[[Image:AbsoluteValueDiagram.svg|thumb|The absolute value of a number may be thought of as its distance from zero.]]
In [[mathematics]], the '''absolute value''' or '''modulus''' of a [[real number]] <math>x</math>, {{nowrap|denoted <math>|x|</math>,}} is the [[non-negative]] value {{nowrap|of <math>x</math>}} without regard to its [[sign (mathematics)|sign]]. Namely, <math>|x|=x</math> if <math>x</math> is a [[positive number]], and <math>|x|=-x</math> if <math>x</math> is [[negative number|negative]] (in which case negating <math>x</math> makes <math>-x</math> positive), and {{nowrap|<math>|0|=0</math>.}} For example, the absolute value of 3 {{nowrap|is 3,}} and the absolute value of −3 is {{nowrap|also 3.}} The absolute value of a number may be thought of as its [[distance]] from zero.

Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the [[complex number]]s, the [[quaternion]]s, [[ordered ring]]s, [[Field (mathematics)|fields]] and [[vector space]]s. The absolute value is closely related to the notions of [[magnitude (mathematics)|magnitude]], [[distance]], and [[Norm (mathematics)|norm]] in various mathematical and physical contexts.