Let X be a set of n distinct points in R^d, where n?3. Prove that one can denote the points of X as x1, . . . , xn in such a way that ?xi?1xixi+1< ?/2 for any i= 2, . . . , n?1.
Added by Tembe N.
Step 1
First, we can choose any point in the set X as x1. Without loss of generality, let's choose the point with the smallest coordinate in the first dimension (if there are multiple points with the same smallest coordinate, choose the one with the smallest coordinate Show more…
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