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Homework Help: Real analysis question

  1. Jan 31, 2010 #1
    Hey guys, got stuck on this question while doing homework. I would appreciate any help.
    Let a,b exist in reals. Show that if a<=b1 for every b1 > b. then a <= b.

    I really got nowhere. I tried letting b1(n)=b+nE where E is a infinitesimal. Then a <= b+nE for all n. Don't really know how to use any axioms here either.
     
  2. jcsd
  3. Jan 31, 2010 #2

    Dick

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    Do a proof by contradiction. Suppose it's NOT true that a<=b. Then a>b. Where is (a+b)/2? Use that for b1. You certainly don't need infinitesimals.
     
  4. Feb 1, 2010 #3
    I think I got it, so a>b, let b1 = (a+b)/2, then b1 > b, but a<= (b1=(a+b)/2). Contradiction
     
  5. Feb 1, 2010 #4

    Dick

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    You've got it.
     
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