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Math Help - Least Element

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    Least Element

    Let n_0\in\mathbb{Z}, S is nonempty subset of T=\left(n\in\mathbb{Z}|n\geq n_0\right) and l* is a the least element of the set T^*=\left(n-n_0+1|n\in S\right). Then  n_0+l+1 is a least element of S.

    I am not sure how to go about this one.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by dwsmith View Post
    Let n_0\in\mathbb{Z}, S is nonempty subset of T=\left(n\in\mathbb{Z}|n\geq n_0\right) and l* is a the least element of the set T^*=\left(n-n_0+1|n\in S\right). Then  n_0+l+1 is a least element of S.

    I am not sure how to go about this one.
    Just show that n_0+l+1 is indeed a lower bound for T and if it weren't the least element that there would be something smaller, and show that this something smaller with a slight modification would be an element of T^* smaller than n_0+l+1.
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