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  1. #1
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    real analysis

    Give an example to show that it is not true ,ingeneral ,that :
    sup(AB)=sup(A)sup(B) and inf (AB)=inf(A)inf(B)
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Hint for the first one:

    A: \: 1,-1,1,-1,...
    B: \: -1,1,-1,1,...
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  3. #3
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    Also consider a_n=\cos\left(\frac{n\pi}{2}\right) and b_n=\sin\left(\frac{n\pi}{2}\right).
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  4. #4
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    Quote Originally Posted by Bruno J. View Post
    hint
    A: \: 1,-1,1,-1,...
    B: \: -1,1,-1,1,...
    But that depends upon how AB is defined.
    If it is defined by AB=\left\{ {xy:x \in A\;\& \,y \in B} \right\} then \sup(A)=\sup(AB)=\sup(B)

    How is AB defined?
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  5. #5
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    Quote Originally Posted by flower3 View Post
    Give an example to show that it is not true ,ingeneral ,that :
    sup(AB)=sup(A)sup(B) and inf (AB)=inf(A)inf(B)
    How about A = \{1,2\},\ B=\{-1,-2\} ?
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