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Math Help - Real Numbers question.

  1. #1
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    Real Numbers question.

    Define a subset A that is a subset the of Real Numbers that satisfies

    1) 1 is an element of A

    2) if n is an element of A then n+1 is an element of A

    yet for which R sub >0 is not a subset of A.


    I can't quite see how to
    use induction in this problem, although I am fairly sure induction
    should be used. Also I am confused as to how since it is given that 1
    is in the set A then how can R sub >0 not be a subset of A?

    If A is a subset of the reals then it can contain any positive or
    negative number. We know 1 is an element of A....

    Help would be appreciated!
    Last edited by mr fantastic; November 1st 2010 at 02:25 PM. Reason: Title.
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  2. #2
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    How about A equals the positive integers?
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  3. #3
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    Well that seems to make sense but how would I go about proving that using induction?
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  4. #4
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    Does the problem statement say that you have to use induction to prove that (2) holds?
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