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

## Keywords:

Division by zero, proof and argumentation, definitions## Abstract

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.

## References

Azzolino, A. (2005). Math spoken here! An arithmetic and algebra dictionary. Retrieved December 16, 2022, from http://www.mathnstuff.com/math/spoken/here/3essay/eun.htm

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 http://mathworld.wolfram.com/DivisionbyZero.html

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

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## How to Cite

*Ohio Journal of School Mathematics*,

*96*(1), 28–34. Retrieved from https://ohiomathjournal.org/index.php/OJSM/article/view/9856

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Copyright (c) 2024 Richard Kaufman