Does anyone have a concrete example of a Cauchy sequence that isnotconvergent?

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- Dec 17th 2009, 03:12 PMplatinumpimp68plus1Cauchy sequence
Does anyone have a concrete example of a Cauchy sequence that is

**not**convergent? - Dec 17th 2009, 04:06 PMKrizalid
i remember i studied once these, and every Cauchy sequence is convergent.

is there any counterexample, because i'm about to die. - Dec 17th 2009, 04:12 PMplatinumpimp68plus1
- Dec 17th 2009, 04:23 PMKrizalid
oh, i'll have to review my notes.

- Dec 17th 2009, 04:33 PMJose27
It all depends on which spaces you're working. For example in working with $\displaystyle \mathbb{R}$ we have that $\displaystyle x_n=\left( 1+\frac{1}{n} \right) ^n$ is convergent, but if you're in $\displaystyle \mathbb{Q}$ this sequence is Cauchy but not convergent.