1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

On divergence

  1. Jan 22, 2014 #1
    Hi folks -- could anyone think of a justification of the idea that if a function's arguments diverge (i.e. are taken to infinity), there's a high probability that the function too will diverge?

    This would be really helpful for thinking about fundamental theories in particle physics, so any help much appreciated!
  2. jcsd
  3. Jan 22, 2014 #2
    Not about "high probability", but if your function is nice enough, complex analysis could be of use. Liouville's theorem at least tells you that non-constant differentiable functions [itex]\mathbb C \to \mathbb C[/itex] are unbounded. I'd guess there's some related machinery that would help more.
  4. Jan 22, 2014 #3


    User Avatar
    Science Advisor

    That statement will make sense if you have some way of "measuring" sets of functions so that you can talk about "probability" in relation to sets of functions.
  5. Jan 22, 2014 #4


    User Avatar
    2017 Award

    Staff: Mentor

    Unbounded, but they don't have to go to infinity. sin(z) for z on the real axis is an example of a function that stays bounded for an argument that goes to infinity.

    I agree with HallsofIvy, without some way to define a probability this does not work.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook