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Math Help - glb and lub (greatest lower bound and least upper bound)

  1. #1
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    glb and lub (greatest lower bound and least upper bound)

    Greetings all,

    I have a question that says S is a bounded set of real numbers and that lub S and glb S are equal. The question wants to know what you can conclude about S (the set).

    my understanding is that glb and lub are both unique numbers and therefore do not equal. The only thing I could think of is that S only contains one number like (0,0) or (5,5) but then I thought maybe in that case there is no glb lub

    thanks
    Paula
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  2. #2
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    Re: glb and lub (greatest lower bound and least upper bound)

    Hey funnybabe.

    The only other thing that builds on top of what you have said is that a set can only contain unique elements (no duplicates). So based on this, what can you say at least about the cardinality of the set?
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  3. #3
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    Re: glb and lub (greatest lower bound and least upper bound)

    the cardinality is 1 so there should only be 1 number in the set?
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  4. #4
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    Re: glb and lub (greatest lower bound and least upper bound)

    Sounds good!
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