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Math Help - Transitive sets.

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
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    Transitive sets.

    Hello, I need a help with the following:

    1. Let $A$ be a transitive set, prove that $A∪{A}$ is also transitive.
    2. Show that for every natural $n$ there is a transitive set with $n$ elements.



    Thank you all!
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  2. #2
    MHF Contributor

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    Re: Transitive sets.

    The term "transitive set" refers to sets of sets: The set, A, is said to be transitive if and only if whenever x\in A and y\in x then y\in A. (Frankly, I had to look that up!)

    Now, if x\in A\cup\{A\}, then either x\in A or x= A. Let y\in x and consider those two cases.

    As for 2, recall Von Neumann's definition of the natural numbers: 0 is the empty set, 1 is the set whose only member is the 0, 2 is the set whose only members are 0 and 1, etc.
    Last edited by Plato; October 27th 2012 at 02:23 PM. Reason: LaTex fix it is not [itex]
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