Dr. J’s Guide to Cardinality

Dr. J introduces the idea of cardinality, the size of a set. Three categories are discussed: finite, countably infinite, and uncountably infinite. Sets with finite size are those where you can count the elements and eventually stop. Sets with countably infinite size can be put into one-to-one correspondence with the natural numbers. Sets with uncountably infinite size have too many elements to be put into one-to-one correspondence with the natural numbers.
These concepts of set size relate to the mathematical treatment of random variables. Discrete random variables can take on finite or countably infinite number of values while continuous random variables can take on uncountably infinite number of values.