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Math Help - Show that the set S defined by 1 Element S... HELP!

  1. #1
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    Exclamation Show that the set S defined by 1 Element S... HELP!

    Show that the set S defined by 1 Element S and s + t Elemeent S whenever s Element S and t Element S is the set of positive integers.

    I do not know how to even start this problem. I know you use induction right? Any other hints?
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  2. #2
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    Quote Originally Posted by mathsucks99 View Post
    Show that the set S defined by 1 Element S and s + t Elemeent S whenever s Element S and t Element S is the set of positive integers.
    As you have presented the question, it is not true.
    Consider: \mathcal{S} = \mathbb{Z}^ +   \cup \left\{ {n + 0.5:n \in \mathbb{Z}^ +  } \right\}.
    Clearly \mathcal{S} has both properties required, contains 1 and is closed with respect to addition.
    But \mathcal{S} \ne \mathbb{Z}^ +.
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  3. #3
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    i dont quite get what your saying. your saying the problem i wrote cannot be true? I use Element for the (element sign) cause i cant type it in...

    Your saying the whole set S cannot be the set of positive integers?
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  4. #4
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    Quote Originally Posted by mathsucks99 View Post
    i dont quite get what your saying. your saying the problem i wrote cannot be true?
    As I have shown the way that you have written the problem it is false.
    I suspect that you want \mathcal{S} \subseteq \mathbb{Z}^ +.
    In which case the statement is true.
    But if you don’t know the difference, how can we possibly help you?
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  5. #5
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    Ok but this is the problem from the homework verbatim:

    Show that the set S defined by 1 ∈ S and s + t ∈ S whenever s ∈ S and t ∈ S is the set of positive integers.

    So i cannot do this answer and should write that down your saying? i dont quite get it obviously.

    Do i use structural induction, recursion?
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