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Math Help - Help with ordinals

  1. #1
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    Help with ordinals

    Prove that if X is a set of ordinals, then supX is an ordinal larger than all elements of X (and therefore not in X).

    Any help would be much appreciated.
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  2. #2
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    Quote Originally Posted by qwe123 View Post
    Prove that if X is a set of ordinals, then supX is an ordinal larger than all elements of X (and therefore not in X).

    Any help would be much appreciated.

    This is false and a good example of what's probably an ill-posed question: for example, the set X=\{1,2\} of the first two ordinals has a maximum which is 2. The same with the set X=\{1,2,7,\omega\}, again we have a maximum which is \omega

    Tonio
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