Am I right to assume one could also sample from a Gaussian distribution for the method to work? Of course, the probability e of sampling between the two real numbers would be very small, but it would be nonzero.
Yes, any distribution with dense support works. Your problem is to prove that your method of number selection really does have a non-zero probability of being between any two distinct reals.
So ... yes, choose from a Gaussian, but then you have to tell me exactly how.
