Their statement makes sense: If you have a non zero probability of something happening, say P, and N times that it could happen, then you would expect it to hap

Their statement makes sense: If you have a non zero probability of something happening, say P, and N times that it could happen, then you would expect it to happen about P * N times. Lets let E = P * N. Now as N goes to infinity the number of times you expect it to happen does as well. Both go to a countable infinity (Aleph 0 as you linked) which is a problem when it comes back to defining P. Normally we would say P = E / N but this doesn't make sense when E and N are both the same 'size' of infinity.