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Math Help - Proof for every Natural number

  1. #1
    jfk
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    Question Proof for every Natural number

    Hi, I'm needing some help with an exercise

    Let A be {k^2|k belongs to N}. I need to if A holds the following proposition: "For every n that belongs to N, if n belongs to A then n+1 belongs to A."
    My problem is on the way the set is defined, as far as I understand it, A should be {1,4,9,16,25,36...}.

    I will appreciate any response as long as it doesn't reveal the solution to the problem... tnx in advance...
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    Re: Proof for every Natural number

    Quote Originally Posted by jfk View Post
    Let A be {k^2|k belongs to N}. I need to if A holds the following proposition: "For every n that belongs to N, if n belongs to A then n+1 belongs to A."
    My problem is on the way the set is defined, as far as I understand it, A should be {1,4,9,16,25,36...}.
    If I were you, I would double check the exact wording of this question.
    As stated, it is false.
    Thanks from jfk
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    jfk
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    Re: Proof for every Natural number

    I'm sorry. I just saw what wrote before (lol).
    What I meant:
    "Let A be {k^2|k belongs to N}. I need to state if A holds or not the following proposition: "For every n that belongs to N, if n belongs to A then n+1 belongs to A."

    By the way A should be {1,4,9,16,25,36...}? is that correct?
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    Re: Proof for every Natural number

    Quote Originally Posted by jfk View Post
    I'm sorry. I just saw what wrote before (lol).
    What I meant:
    "Let A be {k^2|k belongs to N}. I need to state if A holds or not the following proposition: "For every n that belongs to N, if n belongs to A then n+1 belongs to A." By the way A should be {1,4,9,16,25,36...}? is that correct?
    4\in A BUT 4+1\notin A. SO?
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    Re: Proof for every Natural number

    your A is correct (assuming you are working with N_1 and not N_0).

    As written your problem seems very easy (the proposition is false and there is no shortage of counter examples), as plato said...are you sure you have written the question down properly

    edit: didn't see platos post :P
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    jfk
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    Re: Proof for every Natural number

    Thank you all for the responses, now I understand. By the way... if "A" would be the "Empty Set" then the claim will hold since it's a vacuous truth rigth?
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    Re: Proof for every Natural number

    Yes, but your A here is NOT empty so I don't understand why you are asking this.
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