About the definition of "discrete random variable" Hogg and Craig stated that a discrete random variable takes on at most a finite number of values in every finite interval (“Introduction to Mathematical Statistics”, McMillan 3rd Ed, 1970, page 22). This is in contrast with the assumption that discrete data can take on values that are countably infinite, in particular rational numbers (D.W. Gooch: “Encyclopedic Dictionary of Polymers”, App. E, page 980, Springer, 2nd Ed, 2010). I would like to know if discrete random variables can – or can not – take on cuontably infinite values in a finite interval. Or, in other words, if the set of possible values of a discrete random variable may be the set of rational numbers.