1.)does an infinite number of zeroes summed up equal a finite value? 2.)does dx=0? 3.)does 2xdx=0? 4.)the probability of picking 100 in the range of all natural numbers is zero? how can the probability be zero? shouldn't the probability of this be dN? ie.. an infinitesimally small chance? i just don't see how this can be zero.. say you pick a natural number Ni, and you say that this number has a zero probability of being picked, and then you pick any number in the range of natural numbers. One thing for certain is that you WILL pick a number.. so then you end up with Nii, but someone i know says that all the natural numbers have a probability of zero of being picked. but we know we just picked one... so if the probability was truly zero.. why and how did i just pick Nii? how can the answer to number 3 be yes? that would imply that every differential equation e.g: (x+y)dx(x-y)dy=0 would just be zero because (x+y)dx that just equals zero.... (x-y)dy that just equals zero... no work to be done... no reason for naming the damn things... homogeneous odes.... exact equations.... and if 2xdx=0 you're summing up a bunch of zeros how can this EVER reach a finite value other than zero regardless of how many times you're summing it up?