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June 5th, 2013, 12:04 PM  #1 
Newbie Joined: Apr 2013 Posts: 11 Thanks: 0  need help on the proof of the inf on a subset!!
Hi, I tried one exercise question from my text book!! Please correct me if I did something wrong! The questions is about the greatest lower bound!! It is presented right after the Completeness Axiom!! Some parts of the proof is written in the book but there were two parts left as exercise!! Corollary. Every nonempty subset S of R that is bounded below has a greatest lower bound inf S. Proof. Let S be the set S consists of the negatives of the numbers in S. Since S is bounded below there is an m in R such that This implies that Thus S is bounded above by m and there exists sup(S) by the completeness axiom. Let we need to prove (1) and (2) The last two parts were left as exercise. Proof. Part (1) Let This implies that Then Part (2) Assume This implies that which implies that t is an upper bound of S. Since This implies that I think it makes sense but I have many experiences that the proof is wrong even though it makes sense to me!! So please comment on this! 
June 7th, 2013, 01:25 PM  #2  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: need help on the proof of the inf on a subset!! Quote:
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June 7th, 2013, 06:20 PM  #3  
Newbie Joined: Apr 2013 Posts: 11 Thanks: 0  Re: need help on the proof of the inf on a subset!! Quote:
Thank you for your comment!!!  

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