(adsbygoogle = window.adsbygoogle || []).push({}); Suppose (X,d) is a metric space and A, a subset of X, is closed and nonempty. For x in X, define d(x,A) = inf_{a in A}{d(x,a)}

Show that d(x,A) < infinity.

I really don't have much of an idea on how to show it must be finite. An obvious thought comes to mind, namely that a metric is real-valued by definition, so it must be a real number and hence finite, but I don't feel that that reasoning captures the gist of the inherent problem.

Does anyone have any ideas?

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# Homework Help: Problem in a Metric Space!

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