Having probability 0 does not mean it does not occur. Either definition is self-consistent.
To see this more clearly, the probability for any value on an interval [a, b] gets returned by a uniform random distribution on it is 0.
Having probability 0 does not mean it does not occur. Either definition is self-consistent.
To see this more clearly, the probability for any value on an interval [a, b] gets returned by a uniform random distribution on it is 0.