I hate discontinuity in nature. When I graph the probabilities of dice rolls (say, 2 dice or 3 dice) I get integer values that result discrete steps, like a staircase. But I know that the set of points represents a smooth bell curve. How can a set of discrete integer points - each of which is separated by a gaping chasm of an infinite set of fractional numbers - impersonate a smooth continuum? So I keep finding myself asking: is there meaning to the fractional points along the bell curve between the integers? Is there a such thing - at least in principle - as fractional results of dice roills?