Thread: Cauchy sequence w/ unbounded subsequence

Cauchy sequence w/ unbounded subsequence.

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

Originally Posted by really.smarty

Cauchy sequence w/ unbounded subsequence.

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

If you mean in the real or complex numbers then no, it's not posible since every Cauchy sequence converges (in fact this is an iff theorem) and is thus bounded.

Tonio

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.

thank you!