Thread 16837718

I've always wondered this, are there very strange functions or phenomenons that exist such that they behave normally and predictably up until a sudden "large number" then suddenly stops behaving how it used to and becomes chaotic or erratic?

Kind of like the twin prime conjecture, what if it turns out there aren't even infinitely many twin primes past an arbitrary point, that would be so strange, does there exist something like this?

>>16837718 (OP)
let me chatgpt that for you

>>16837718 (OP)
Define "big"
x^2 is smaller than x for x<1 and larger than x for x>1

ie. 3 body problem
Just read about chaotic systems.

>>16837718 (OP)
yes, and you don't have to go high numbers for it

>>16837736
why do we then pretend that limiting processes work out?

>>16837988
we started this madness when Cantor dipped his feet into the pool of infinity. we don't really know shit about the behaviour of infinity, it's all assumptions

Consider the function [math]tan(2^ {0.001(x^{2})})[/math]. When you put in into Wolfram, it does what you want

>>16837718 (OP)
You mean like having a big peepee vs having a small peepee?

>>16837728
Heaviside's left side is heavy.

>>16837996
does this apply to calculus? infinity is all over the place in there, either in the guise if the infinitely small or literally in the notation (Riemann sum definition of the integral)

>>16837736

>What the Christ happens when lambda gets bigger than the point of accumulation?

--Robert May (1936-2020), on a blackboard at University of Sydney