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Math Help - Provide a recursive definition of the following sets

  1. #1
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    Provide a recursive definition of the following sets

    I have some definitions that would apply to these, but I'm not sure whether or not they are very concrete, and I would also like to confirm that they are correct. Here are the sets and my current answers.

    a) The set of odd positive numbers.
    1\in S
    If x\in S, then x+2\in S

    b) The positive integer powers of 3.
    3\in S
    If x\in S, then 3\times x\in S

    c) The positive multiples of 4.
    4\in S
    If x\in S, y\in S, then x+y\in S

    Are these all accurate, or would they benefit from more detailed answers?
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  2. #2
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    You've got the right idea, but it might be useful to use a bit different notation, since a recursion is asked for. Something like this for c) maybe:

    Let S be the set of positive multiples of 4.
    s_n \in S
    s_0 = 4
    s_n = s_{n-1} + 4
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