- #1
aodesky
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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) = infa 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?
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?