An Argument for a New Description of “Division by Zero”



Division by zero, proof and argumentation, definitions


Instead of simply characterizing division by zero as “undefined” to students, we argue that it should be considered on the basis of mathematically consistent equations. Division by zero leads to inconsistent mathematical statements that are just as invalid as other incorrect statements. We propose that division by zero should be characterized as “inconsistent” rather than “undefined.” Consistency underlies the fundamental truth of all mathematical equations and the interrelationships between mathematical objects.


Azzolino, A. (2005). Math spoken here! An arithmetic and algebra dictionary. Retrieved December 16, 2022, from

Burton, D. M. (2007). The history of Mathematics: An introduction (6th ed.). McGraw-Hill.

Dell, D. (Ed.). (1996). World book encyclopedia: The world book of math power 1: Learning math. World Book.

Derbyshire, J. (2004). Prime obsession: Bernhard Riemann and the greatest unsolved problem in mathematics. Penguin.

Gowers, T. (Ed.). (2008). The Princeton companion to mathematics. Princeton University Press.

Kaplan, R. (1999). The nothing that is: A natural history of zero. Oxford University Press.

Weisstein, E. W. (n.d.). Division by zero. MathWorld–A Wolfram web resource. Retrieved December 16, 2022, from

Youse, B. K. (1971). Arithmetic: An introduction to mathematics. Canfield Press.




How to Cite

Kaufman, R. (2024). An Argument for a New Description of “Division by Zero”. Ohio Journal of School Mathematics, 96(1), 28–34. Retrieved from




Similar Articles

1 2 > >> 

You may also start an advanced similarity search for this article.