The digits of pi never repeat because it can be proven that π is an irrational number and irrational numbers don’t repeat forever. If you write out the decimal expansion of any irrational number (not just π) you’ll find that it never repeats. That means that π is irrational, and that means that π never repeats. If a number can be written as the D digit number “N” repeating forever, then it can be expressed as . Now define a function , where n is some positive integer, and that excited n, n!, is “n factorial“.