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Math Help - Induction: show a finite set of reals has a maximal/minimal element

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    Induction: show a finite set of reals has a maximal/minimal element

    Use induction to show that every finite set of real numbers has a maximal element
    and a minimal element.

    I was thinking about using well-ordering principle for minimal however how do I use induction on this one?
    Last edited by CaptainBlack; December 13th 2010 at 03:19 AM. Reason: thread title
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  2. #2
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    Quote Originally Posted by mathsohard View Post
    Use induction to show that every finite set of real numbers has a maximal element
    and a minimal element.

    I was thinking about using well-ordering principle for minimal however how do I use induction on this one?
    Trivially true if the set has a single element.

    Suppose it true for sets with k elements.

    Then for a set with k+1 elements you may partition the set into a set A with k elements and a singleton, ...

    CB
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