Thread: Write this in fopa lang?

if k is any natural numb, then n^3>kn^2 for all sufficent large n.

Originally Posted by ikurwae89

if k is any natural numb, then n^3>kn^2 for all sufficent large n.

What does "Write this in fopa lang?" mean?

first order penos arithmetic

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

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?

((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 (one can also use >= instead of > here).

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

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.