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Thread: Bounded above and bounded below

  1. #1
    Junior Member
    Apr 2010

    Bounded above and bounded below


    See Q3 on attatched document. Im preparing for a forthcoming exam and always struggle with these type of questions....

    for (i) i got: bounded above = yes; LUB = 1; In set = YES; Bounded Below = YES; GLB = 0; In set = no;

    Im more confident on this part but not for the other parts. Any help/guidance?
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  2. #2
    Senior Member
    May 2010
    Los Angeles, California
    For 3(iv) we have $\displaystyle -\sqrt 11 < x < \sqrt 11$. LUB is $\displaystyle \sqrt 11$ and GLB is $\displaystyle -\sqrt 11$. This is because the rationals are dense in $\displaystyle \Bbb R$. Neither of these numbers are rational because 11 is prime.
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