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How can arbitrarily large primes be applied to limit

Is there any connection between an infinite set limit like prime numbers and differentiation and differentiability?

x(infinite set of possible variables) would change with respect to y(infinite set of possible variables) on which it has a functional relationship.

Also where does probability play specifically in mathematical analysis? In probability theory what happens when the sample space is infinite ? I have been trying to make sense of this with fourier transform and measure theory of infinite intersections/ unions. Does anyone have any links that I can use to familiarize myself more with these concepts? Thanks in advance.

:uhh: