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Supremum question

  1. Nov 15, 2008 #1

    I'm trying to prove that b^{r+s}=b^r*b^s for any real r,s where b^r = sup{b^t:t \leq r} and t is rational. (This is prob 1.6f in Rudin)

    My question. Can one show that for two sets X and Y:

    sup(XY)=(supX)(supY) where XY = {x*y: x\in X, y\in Y}

  2. jcsd
  3. Nov 15, 2008 #2


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    Try playing with positive and negative numbers.
  4. Nov 15, 2008 #3
    => Counterexample very easy
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