Question: Let (xn) be a sequence that converges to x. Show that the points of (xn) become arbitrarily close to one another in the sense that

Let (xn) be a sequence that converges to x. Show that the points of (xn) become arbitrarily close to one another in the sense that for every ε > 0 there exists an N such that
p(xm, xn) < e for all m, n > N

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