# Prove sequence is bounded

1. Nov 11, 2007

### zachsdado

1. The problem statement, all variables and given/known data

prove that a monotone sequence which has a bounded subsequence is bounded

2. Relevant equations

3. The attempt at a solution

2. Nov 11, 2007

### sprint

did you even try to solve this?

3. Nov 11, 2007

### zachsdado

Of course

I tried using the def. of a monotone sequence to show that the subsequence was monotone and bounded hence it converged to some number and then tried to prove that the sequence was convergent thus it was bounded

4. Nov 11, 2007

### ZioX

The problem is of course that there could be a lot of convergent subsequences. Try taking the sup of the limits over all of the convergent subsequences. Claim: the sequence converges to this sup.

I think this should do it.

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