Editing Probability distribution (section)

===Cumulative distribution function===
A real-valued discrete random variable can equivalently be defined as a random variable whose cumulative distribution function increases only by [[jump discontinuity|jump discontinuities]]—that is, its cdf increases only where it "jumps" to a higher value, and is constant in intervals without jumps. The points where jumps occur are precisely the values which the random variable may take.
Thus the cumulative distribution function has the form
<math display="block">F(x) = P(X \leq x) = \sum_{\omega \leq x} p(\omega).</math>
The points where the cdf jumps always form a countable set; this may be any countable set and thus may even be dense in the real numbers.