what is base with absolute difference
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Answer:
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.
Showing the absolute difference of real numbers x and y as the distance between them on the real line.
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 or 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.
Step-by-step explanation:
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.
Showing the absolute difference of real numbers x and y as the distance between them on the real line.
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 or 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.