(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let F be an ordered field in which every strictly monotone increasing sequence bounded above converges. Prove that F is complete

2. Relevant equations

Definitions:

Monotone Sequence property:

Let F be an ordered field. We say that F has the monotone sequence property if every monotone increasing sequence bounded above converges.

Completeness Property:

An ordered field is said to be complete if it obeys the monotone sequence property

3. The attempt at a solution

Approach 1

I'm not sure what exactly to prove. The question says that "strictly monotone increasing sequence bounded above converges" which is pretty much the monotone sequence property. And by the completeness property, F is complete . So what exactly am I supposed to do ? It seems trivial.

Approach 2

I could also get any strictly increasing sequence and extract an increasing subsequence which is bounded above and thus converges by monotone sequence property

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# Homework Help: Prove that F is complete

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