Could anyone give me a specific example of Cauchy Sequence in Metric Space X that does not converge?

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- October 29th 2009, 02:41 AMfelixmcgradyCauchy Sequences
Could anyone give me a specific example of Cauchy Sequence in Metric Space X that does not converge?

- October 29th 2009, 03:02 AMRebesques
Consider with the hereditary topology from and check .

- October 29th 2009, 08:44 AMHallsofIvy
Or, let X be the set of

**rational**numbers with the "usual metric", d(x,y)= |x-y|. Take the sequence 3, 3.1, 3.14, 3.1415, 3.14159, 3.141592, ... where the nth term is the decimal expansion of to n-1 decimal places. It is easy to see that this sequence is a Cauchy sequence and that it does not converge in the rational numbers. - November 30th 2009, 05:54 PMtalb1mnk7Cauchy Sequences