Cauchy sequence w/ unbounded subsequence.

Is this possible? If so give an example, otherwise argue how it would be impossible?

Printable View

- November 13th 2009, 12:13 PMreally.smartyCauchy sequence w/ unbounded subsequence
Cauchy sequence w/ unbounded subsequence.

Is this possible? If so give an example, otherwise argue how it would be impossible? - November 13th 2009, 01:26 PMtonio
- November 13th 2009, 01:40 PMDeadstar
I think there's different answers to this question depending on whether you are in a metric space but I'll assume not...

Here's a theorem for you.

Any Cauchy sequence is bounded.

Ill post up a proof if you need me to but basically just use the definition of a Cauchy sequence to show it converges.

Since any Cauchy sequence is bounded, its subsequences must be bounded. - November 13th 2009, 04:58 PMreally.smarty
thank you!