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Math Help - Induction Set Proof

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    Induction Set Proof

    Prove the following theorem

    If G is a collection of induction sets, then the intersection of all the sets in G is an induction set.
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  2. #2
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    Quote Originally Posted by noles2188 View Post
    Prove the following theorem

    If G is a collection of induction sets, then the intersection of all the sets in G is an induction set.


    Since all G_i are all inductive  1\in G_{1}\wedge 1\in G_{2}\wedge 1\in G_{3} and............................................ 1\in G_{n} =====> 1\in\bigcap G_i.

    Suppose now k\in\bigcap G_i ====> k\in G_{1}\wedge k\in G_{2}\wedge k\in G_{3} and........................................... k\in G_{n}====> k+1\in G_{1}\wedge k+1\in G_{2}\wedge k+1\in G_{3} and............................................... .. k+1\in G_{n}=====> k+1\in\bigcap G_i

    Hence \bigcap G_i is inductive
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