(adsbygoogle = window.adsbygoogle || []).push({}); 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:

-{b_{n}} 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Sequence Proof (Am I missing something here?)

Loading...

Similar Threads for Sequence Proof missing |
---|

I Convergence of ##\{\mathrm{sinc}^n(x)\}_{n\in\mathbb{N}}## |

I Convergence of a recursively defined sequence |

B Proof of a limit rule |

I What is this sequence that converges to ln(x) called? |

**Physics Forums | Science Articles, Homework Help, Discussion**