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Math Help - Induction Statements

  1. #1
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    Induction Statements

    I'm trying to find an example of a statement S(n) that is true for all natural numbers n but for which the assumption that S(k) is true from some k is not needed to show that S(k+1) is true.

    Any ideas?
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  2. #2
    Senior Member
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    I guess you mean: It is not required to show S(0) and to show S(k) implies S(k+1).

    Let S be:

    n = n
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