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Math Help - Real Numbers

  1. #1
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    Real Numbers

    Mark each true or false and justify.

    1) If a nonempty subset of real numbers has an upper bound, then it has a least upper bound.

    2) Every nonempty bounded subset of real numbers has a maximum and a minimum.

    3) If m is an upper bound for S and m' < m, then m' is not an upper bound for S.

    4) For each real number x and each E > 0, there exists an n element of the natural numbers such that nE > x.
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  2. #2
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    Quote Originally Posted by noles2188 View Post
    1) If a nonempty subset of real numbers has an upper bound, then it has a least upper bound.
    How about (-\infty,0]?

    2) Every nonempty bounded subset of real numbers has a maximum and a minimum.
    How about (-1,1)?

    3) If m is an upper bound for S and m' < m, then m' is not an upper bound for S.

    How about (-1,1) and m=1 and m'=2?

    4) For each real number x and each E > 0, there exists an n element of the natural numbers such that nE > x.
    Yes
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