Yes, no such thing as continuity in the real world, real number are not physically real. Buuut, they are very useful for making computations easiers. I never disqualified the utility of the gaussian distribution, I simply pointed out the obvious that Gaussian != Uniform > the expression "cryptographic hash function" itself implies apparent continuity of distribution. No, it implies apparent uniformity of disitribution. Continuity is another (topological) property. f^(-1) (A) is an open set for every open set A.