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(Solved): Let (X,d) be a metric space and let (xk)k and (yk)k be Cauchy sequences in X. Consider the sequence ...
Let (X,d) be a metric space and let (xk)k and (yk)k be Cauchy sequences in X. Consider the sequence (?k)k of real numbers defined by
(See figure)
Show that (?k)k converges.
Caution: it is not assumed that (X, d) is complete!
'.'
?? ?k = d(xk, ??) font ? k = 1, 2,...
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