Lemma 13 (Cauchy sequence in finite space is eventually constant). Let (F,d) be a metric space,

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1. Since F is a finite set, there must be a finite number of elements in F. Let&#x27;s denote the num

Lemma 13 (Cauchy sequence in finite space is eventually constant). Let (F,d) be a metric space, with F a finite set, and let (a_n) be a Cauchy sequence in F. Then (a_n) is eventually constant. Complete the proof here