Computational and Experimental Methods for Identifying Nonsensical Equations and Inequalities

Nenad Stojanović () and Bharath Sriraman ()
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Nenad Stojanović: University of Kragujevac, Faculty of Science
Bharath Sriraman: University of Montana – Missoula, Department of Mathematical Sciences

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 675-701 from Springer

Abstract: Abstract In contemporary education, increasing importance is placed on the development of critical thinking and the ability to precisely analyze mathematical terms. This chapter focuses on experimental and computational approaches to the study of meaningful and nonsensical equations and inequalities, with the aim of enhancing the understanding of the logical structure of mathematical formulas. Special emphasis is placed on the concept of a formula’s domain, as well as on the truth set – the set of values for which the formula has a defined meaning or validity. Through graphical representations, we analyze the behavior of different types of formulas, examining their logical properties and their role in the educational process. We demonstrate how visual and computational tools can assist in identifying terms that lack clear meaning, whether due to an improperly defined domain, inconsistencies in the structure of the formula, or the absence of a truth set. Attention is also drawn to the problematic use of general formulas for solving irrational inequalities without prior analysis of the conditions under which they apply. The goal of this chapter is to emphasize the importance of accurately interpreting the meaning of mathematical terms and to highlight the need for the development of a methodology that distinguishes formally correct but nonsensical terms from those that are logically and educationally well-founded.

Keywords: Proposition; Term; Formula; Domain; Truth set; Irrational inequalities (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16368-4_74

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DOI: 10.1007/978-3-032-16368-4_74

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