Definition 5.2.5. Countable and Uncountable Sets.
\(R\) contains a countable number of points if either \(R\) is finite or there is a one to one correspondence between R and the positive integers. Such a set will be called discrete. We will see that often the set \(R\) is not countable. If \(R\) consists of an interval of points (or a union of intervals), then we call X a continuous random variable.