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Math Help - Proving that sup S \leq inf T

  1. #1
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    Proving that sup S \leq inf T

    Given the following, I need to show that  sup S \leq  inf T. Let S and T be nonempty subsets of  \mathbb{R} \backepsilon s \leq t \forall s \in S \wedge t \in t.
    A) Observe that S is bounded above and that T is bounded below.
    B) Prove that  sup S \leq inf T.
    C) Given an example of such sets S and T where  S \cap T \neq \varnothing.
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  2. #2
    Member Black's Avatar
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    (b) follows immediately from the definitions of sup and inf.

    (c) Let S=[0,1/2] and T=[1/2,1].
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