Don't need a proof, just need confirmation.

Every cauchy sequence converges. This is true right?

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- October 24th 2006, 03:26 PMJaysFan31Cauchy sequence
Don't need a proof, just need confirmation.

Every cauchy sequence converges. This is true right? - October 24th 2006, 03:31 PMPlato
If you are working in the real number field then that is correct.

It is correct in any complete metric space. - October 24th 2006, 04:36 PMThePerfectHacker
- October 24th 2006, 05:03 PMPlato
Actually you are correct to ‘call my hand’ on that.

In most treatments a*complete space*is one in which every Cauchy sequence converges. Thus, in some way my answer is circular.

In my own defense, some texts that is equivalent to*every infinite bounded set has a limit point.*