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- Absolute_difference abstract "The absolute difference of two real numbers x, y is given by |x − y|, the absolute value of their difference. It describes the distance on the real line between the points corresponding to x and y. It is a special case of the Lp distance for all 1 ≤ p ≤ ∞ and is the standard metric used for both the set of rational numbers Q and their completion, the set of real numbers R.As with any metric, the metric properties hold: |x − y| ≥ 0, since absolute value is always non-negative. |x − y| = 0 if and only if x = y. |x − y| = |y − x| (symmetry or commutativity). |x − z| ≤ |x − y| + |y − z| (triangle inequality); in the case of the absolute difference, equality holds if and only if x ≤ y ≤ z.By contrast, simple subtraction is not non-negative or commutative, but it does obey the second and fourth properties above, since x − y = 0 if and only if x = y, and x − z = (x − y) + (y − z).The absolute difference is used to define other quantities including the relative difference, the L1 norm used in taxicab geometry, and graceful labelings in graph theory.When it is desirable to avoid the absolute value function – for example because it is expensive to compute, or because its derivative is not continuous – it can sometimes be eliminated by the identity|x − y| < |z − w| if and only if (x − y)2 < (z − w)2.This follows since |x − y|2 = (x − y)2 and squaring is monotonic on the nonnegative reals.".
- Absolute_difference thumbnail Absolute_difference.svg?width=300.
- Absolute_difference wikiPageID "28021681".
- Absolute_difference wikiPageRevisionID "542816857".
- Absolute_difference hasPhotoCollection Absolute_difference.
- Absolute_difference title "Absolute Difference".
- Absolute_difference urlname "AbsoluteDifference".
- Absolute_difference subject Category:Real_numbers.
- Absolute_difference type Abstraction100002137.
- Absolute_difference type ComplexNumber113729428.
- Absolute_difference type DefiniteQuantity113576101.
- Absolute_difference type Measure100033615.
- Absolute_difference type Number113582013.
- Absolute_difference type RealNumber113729902.
- Absolute_difference type RealNumbers.
- Absolute_difference comment "The absolute difference of two real numbers x, y is given by |x − y|, the absolute value of their difference. It describes the distance on the real line between the points corresponding to x and y. It is a special case of the Lp distance for all 1 ≤ p ≤ ∞ and is the standard metric used for both the set of rational numbers Q and their completion, the set of real numbers R.As with any metric, the metric properties hold: |x − y| ≥ 0, since absolute value is always non-negative.".
- Absolute_difference label "Absolute difference".
- Absolute_difference label "Diferença absoluta".
- Absolute_difference label "فرق مطلق".
- Absolute_difference sameAs Diferença_absoluta.
- Absolute_difference sameAs m.0ch0xxw.
- Absolute_difference sameAs Q1773230.
- Absolute_difference sameAs Q1773230.
- Absolute_difference sameAs Absolute_difference.
- Absolute_difference wasDerivedFrom Absolute_difference?oldid=542816857.
- Absolute_difference depiction Absolute_difference.svg.
- Absolute_difference isPrimaryTopicOf Absolute_difference.