(b) Beweisen Sie, dass eine Abbildung d: A× A →→→→R genau dann eine Metrik auf der Menge A ist, wenn (4 P.) Vx, yЄA: d(x,y) = 0 ⇒ x=y (1) und Vx, y, z ЄA: d(x, y) ≤ â(z, x) + d(y, z) (2) gelten.
(b) Beweisen Sie, dass eine Abbildung d: A× A →→→→R genau dann eine Metrik auf der Menge A ist, wenn (4 P.) Vx, yЄA: d(x,y) = 0 ⇒ x=y (1) und Vx, y, z ЄA: d(x, y) ≤ â(z, x) + d(y, z) (2) gelten.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
Question
prove that a formation d:AxA->R is a metric on the set a if and only if (1) and (2) apply
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