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Handsome calculus n00b seeks reassuring relationship with numbers.

  1. Aug 2, 2006 #1
    Hi peeps! I have some minor calculus problem, well confusion is the problem.

    I was playing about with some numbers while doing some differential calc problems, when i started to explore a little further one expression.

    [/tex] ----- (1)

    Of course i thought about rational numbers and primes, and that a rational number is any number which can be expressed as the quotient of two integers.

    So assuming:
    [tex]n \in Z^+[/tex]
    [tex]m \in Z^+[/tex]

    I then thought about what if the exponent was a prime, so
    [tex]\frac{p}{m}[/tex] where [tex]p=prime[/tex]

    Then for:
    [tex]1 < m < p[/tex]
    The exponent would allways be irrational.

    Upon seeing the inequality expresison i wrote down i wondered if there was a link between it and the triangle inequality expression. Is this the case?
    Last edited: Aug 2, 2006
  2. jcsd
  3. Aug 2, 2006 #2
    god title, but i think its puting people off
  4. Aug 2, 2006 #3
    story of my life that :cry:
  5. Aug 2, 2006 #4


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    Homework Helper

    The last equality isn't true. Do you want:



    [tex]\sqrt[m]{\frac{1}{n}}=n^{-1/m}[/tex] ?

    What does this mean? The exponent is p/m, which is rational when m is rational. Are you saying the function is irrational? This depends on which of the above two functions you're talking about.

    I don't see what you mean. What kind of link are you thinking of?
    Last edited: Aug 2, 2006
  6. Aug 2, 2006 #5
    Oops i forgot the x, sorry im latex illiterate. I meant the first correction, edited my post.

    Ok ill re-phrase the post to clear things up, apologies.
  7. Aug 2, 2006 #6
    hmm nevermind, its best you all forget i ever posted this......i feel so stupid now :blushing: :redface:
  8. Aug 2, 2006 #7
    It doesn't work. If x = 27, p = 7 and m = 3, then x ^(-p/m) = 27 ^(-7/3) = 1/3^7. None of these are irrational.
  9. Aug 2, 2006 #8
    Yes, ok dont rub it in :rofl:
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