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Math Help - Write this in fopa lang?

  1. #1
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    Write this in fopa lang?

    if k is any natural numb, then n^3>kn^2 for all sufficent large n.
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  2. #2
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    Quote Originally Posted by ikurwae89 View Post
    if k is any natural numb, then n^3>kn^2 for all sufficent large n.
    What does "Write this in fopa lang?" mean?
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  3. #3
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    first order penos arithmetic
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  4. #4
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    \forall k\exists m\forall n.\,n\ge m\to n^3>kn^2

    If >= is not considered a part of the language of PA, then it can be replaced using the following equivalence.

    \forall n\forall m.\,n\ge m\leftrightarrow\exists p.\,n=m+p
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  5. #5
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    can u explain to me how u got that?

    This is what i got.

    ((For all k)( there exists m)( there exists n)(n.n.n > k.m.m.m))
    i dont have the upside A and E.

    sorry

    what is the difference?
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  6. #6
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    ((For all k)( there exists m)( there exists n)(n.n.n > k.m.m.m))
    (1) The original problem says "for all sufficent large n," while your formula says "there exists n."

    (2) I don't understand why you replaced "n^3 > kn^2" with "n^3 > km^3."

    (3) "For all sufficiently large n" means "for all n that exceed a certain lower bound m." That's why I said \exists m\forall n.\,n>m\to\dots (one can also use >= instead of > here).
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  7. #7
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    sorry about my stuff up and thanks for making the for all sufficient large n clear

    so this is how you would write it.

    ((For all k)( there exists m)( for all n)(n>=m)--> (n.n.n > k.n.n.))


    Thanks a lot btw really helpful
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  8. #8
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    so this is how you would write it.

    ((For all k)( there exists m)( for all n)(n>=m)--> (n.n.n > k.n.n.))
    Yes.
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