What Is 1/0 from the Practical Viewpoint: A Pedagogical Note

Abstract

What is 1/0: Students are first taught—in elementary school—that it is undefined, then—in calculus—then it is infinity. In both cases, the answer is usually provided based on abstract reasoning. But what about the practical meaning? In this paper, we show that, depending on the specific practical problem, we can have different answers to this question: in some practical problems, the correct answer is that 1/0 is undefined, in others, the correct answer is that $1/0=0$—and there are probably other practical problems where we can have different answers. Bottom line: there is no unversal answer, the correct answer depends on what practical problem we are considering.