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Math Help - [SOLVED] Proof regarding maximums and minimums of ordered sets

  1. #1
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    [SOLVED] Proof regarding maximums and minimums of ordered sets

    Let U be an ordered set.

    Prove the following:
    The minimum of U, if it exists, is unique. The maximum of U, if it exists, is unique.

    Any advice? Thanks in advance.
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  2. #2
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    Ordered set

    Hello jzellt
    Quote Originally Posted by jzellt View Post
    Let U be an ordered set.

    Prove the following:
    The minimum of U, if it exists, is unique. The maximum of U, if it exists, is unique.

    Any advice? Thanks in advance.
    Let m_1 and m_2 be two minima of U. Then

    \forall x \in U, m_1 \le x \wedge m_2 \le x

    \Rightarrow m_1 \le m_2 \wedge m_2 \le m_1

    \Rightarrow m_1 = m_2

    Same with maxima.

    Grandad
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