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Math Help - Supremum and Infima

  1. #1
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    Supremum and Infima

    Hi all,

    Given a set:
    x \in (-\infty, -2] \cup [-1, \infty)
    would you say that, the least upper bound and greatest lower bound do not exist.
    and subsequently for:
    x \in (\frac{-\sqrt{29}}{2}+\frac{3}{2}, \frac{\sqrt{29}}{2}+\frac{3}{2}), That the least upper bound is (\frac{\sqrt{29}}{2}+\frac{3}{2}) and the lower bound is (\frac{-\sqrt{29}}{2}+\frac{3}{2})
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Oiler View Post
    Given a set:
    x \in (-\infty, -2] \cup [-1, \infty)
    would you say that, the least upper bound and greatest lower bound do not exist.
    and subsequently for:
    x \in (\frac{-\sqrt{29}}{2}+\frac{3}{2}, \frac{\sqrt{29}}{2}+\frac{3}{2}), That the least upper bound is (\frac{\sqrt{29}}{2}+\frac{3}{2}) and the greatest lower bound is (\frac{-\sqrt{29}}{2}+\frac{3}{2})
    Yes to both questions. When you specify a set, write just (-\infty, -2] \cup [-1, \infty), not x \in (-\infty, -2] \cup [-1, \infty).

    Nice nickname, Euler.
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