Absolute difference - Wikipedia Absolute difference Showing the absolute difference of real numbers x and y as the distance between them on the real line. 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 L 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 L 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 ) < ( z − w ). This follows since x − y = ( x − y ) and squaring is monotonic on the nonnegative reals. See also Absolute deviation References Weisstein, Eric W. `` Absolute Difference ''. MathWorld. This algebra - related article is a stub. You can help Wikipedia by expanding it. Retrieved from `` https://en.wikipedia.org/w/index.php?title=Absolute_difference&oldid=748599984 '' Categories : Real numbers Algebra stubs Talk About Wikipedia Norsk Português Edit links This page was last edited on 9 November 2016, at 02 : 52. Text is available under the Creative Commons Attribution - ShareAlike License ; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia ® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. About Wikipedia

Question: the difference of the absolute value of two numbers
Answer: absolute difference