Okay so I have the following problem: Let P be some probability function such that (N,P(N)) is a probability space with said function, with P(N) being parts of N. Find a probability function Q in (N, P(N)), such that Q $\neq$ $P_X$ for every random variable X: N $\to$ N given.
I'm trying something similar to the diagonalization argument that proofs the rationals are not numerable using decimal expansion. Namely, if I enumerate every random variable as $X_n$, creating a new random variable that sends n to $X_n(n)+1$. Then I "assume" that the associated probability function $P_X$ is different to every ${P_X}_n$. Problem is this only demonstrates that the set of random variables X: N $\to$ N is not countable.