# Sequence Proof (Am I missing something here?)

1. Nov 2, 2009

### Newtime

Sequence Proof (Am I missing something here??)

The reason I'm posting this is because I just took an exam and this was one of the questions, and it was so easy I feel like I may have been completely overlooking a complicating factor:

-{bn} is a sequence of positive real numbers. prove that either it contains a convergent subsequence or converges to positive infinity.

proof.

two case: either the sequence is bounded or unbounded. if it is bounded, apply the bolzano-weirstrass theorem to conclude that it contains a convergent subsequence. if unbounded, by definition, the sequence goes to positive infinity.

qed

On the exam I used better notation and wording but that's it essentially. so what's the consensus...is this valid?

2. Nov 2, 2009

### l'Hôpital

Re: Sequence Proof (Am I missing something here??)

lol nvm. Misread.

3. Nov 2, 2009

### mathman

Re: Sequence Proof (Am I missing something here??)

The unbounded case is more complicated. It might have a subsequence which "converges" to infinity, as well as another subsequence which is convergent to a finite number.

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