
#1
Jan2214, 02:06 PM

P: 115

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
Jan2214, 02:38 PM

P: 206

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 nonconstant differentiable functions [itex]\mathbb C \to \mathbb C[/itex] are unbounded. I'd guess there's some related machinery that would help more.




#3
Jan2214, 02:45 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,885





#4
Jan2214, 02:48 PM

Mentor
P: 10,813

On divergenceI agree with HallsofIvy, without some way to define a probability this does not work. 


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