# Thread:

1. ## Cauchy sequence

Does anyone have a concrete example of a Cauchy sequence that is not convergent?

2. i remember i studied once these, and every Cauchy sequence is convergent.

is there any counterexample, because i'm about to die.

3. Originally Posted by Krizalid
i remember i studied once these, and every Cauchy sequence is convergent.

is there any counterexample, because i'm about to die.
Every convergent series is Cauchy... but in general, the converse isn't true. Only in R.

4. oh, i'll have to review my notes.

5. Originally Posted by platinumpimp68plus1
Does anyone have a concrete example of a Cauchy sequence that is not convergent?
It all depends on which spaces you're working. For example in working with $\mathbb{R}$ we have that $x_n=\left( 1+\frac{1}{n} \right) ^n$ is convergent, but if you're in $\mathbb{Q}$ this sequence is Cauchy but not convergent.
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