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Math Help - prove or disprove question about two natural number

  1. #1
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    prove or disprove question about two natural number

    prove or disprove : for all M, N in natural number , M < N => (exists some number K in natural number ,such that M < K and k < N)
    I notice that this is a false statement which i need to proof the negation of statement to disprove it.
    so far i got ,

    for all M , N in natural number , M < N => (for all number K in natural number , that M => K or K <= N)
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    Re: prove or disprove question about two natural number

    Quote Originally Posted by amazingboxz View Post
    prove or disprove : for all M, N in natural number , M < N => (exists some number K in natural number ,such that M < K and k < N)
    I notice that this is a false statement which i need to proof the negation of statement to disprove it.
    so far i got , for all M , N in natural number , M < N => (for all number K in natural number , that M => K or K <= N)
    Well \{1,2\}\subset\mathbb{N}~\&~1<2, what natural number is between them?
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    Re: prove or disprove question about two natural number

    no natural number can be exists in between 2 Consecutive Numbers , that is why i think this is false statement and need to be disprove
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    Re: prove or disprove question about two natural number

    Quote Originally Posted by amazingboxz View Post
    no natural number can be exists in between 2 Consecutive Numbers , that is why i think this is false statement and need to be disprove
    Don't you understand that disproves the statement?
    One counter-examples is sufficient to disprove a statement.
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    Re: prove or disprove question about two natural number

    here is the problem , my prof haven't mention any thing about disprove the statement using counter example and I'm not sure we are allow to use counter-example in this assignment that why i'm struggling.
    Anyway thanks for the help , very appreciated

    P.S , the reason is because in this course , we are required to construct a proof structure to obtain full mark. which means that we can't just simply provide a counter-example .
    Last edited by amazingboxz; March 3rd 2013 at 07:54 PM.
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    Re: prove or disprove question about two natural number

    I hope maybe this will help in general.

    prove or disprove question about two natural number-mhfproofhelp.png
    Thanks from amazingboxz
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    Re: prove or disprove question about two natural number

    Quote Originally Posted by amazingboxz View Post
    here is the problem , my prof haven't mention any thing about disprove the statement using counter example and I'm not sure we are allow to use counter-example in this assignment that why i'm struggling.
    Anyway thanks for the help , very appreciated
    P.S , the reason is because in this course , we are required to construct a proof structure to obtain full mark. which means that we can't just simply provide a counter-example .
    Surely none of the above is true. No competent mathematics professor would have failed to point out a basic fact of proof-theory. You must have misunderstood the professor.

    Did you miss class the day basic proof-theory was explained? Surely you have heard it said: "we cannot prove a negative"?
    However, we can disprove a positive by giving one counter-example. If someone says "all continuous functions have derivatives", you disprove the statement pointing out f(x)=|x| is continuous but has no derivative at x=0.

    Now if I am not incorrect about your take on this instructor, then you need to have a sit down discussion with the department chair about this. As a retired university mathematics chair I can tell how important that can be. BUT don't do it it if your facts are not in order.
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