Let x, y, and z be points in Rn. Prove that distance has the following properties. (a)

Chapter 1, Problem 39

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Let x, y, and z be points in Rn. Prove that distance has the following properties. (a) d(x, y) 0 (b) d(x,y) = Oifand onlyifx = y (c) d(x, z) ::5 d(x, y) + d(y, z) These properties are used as axioms to generalize the concept of distance for certain spaces.

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