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Math Help - Proof of non-empty subsets, glb and lub

  1. #1
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    Proof of non-empty subsets, glb and lub

    Let S be a non-empty subset of R and Suppose there is a non-empty set of T subset of S.
    a) Prove: if S is bounded above, then T is bounded above and lub t< or = lub S.

    b) Prove: if S is bounded below, then T is bounded below and glbT is > or = glbS.

    I am having a really hard time with this.
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  2. #2
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    Zagreb
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    a) if S is bounded above ---> exist supremum of S ---> that means that
    sup( S ) >= every element of S and that means that sup( S ) >= every
    element of T ( T is bounded above ) ---> exist supremum of T and sup( S ) >= sup( T )

    b) look at a) part and you can figure it out
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