for the learning of mathematics

an international journal of mathematics education

Pessia Tsamir ,  Dina Tirosh - Vol. 45 Num. 1 (2025)
 Nonequivalent definitions: anecdotal incidents or an ordinary constancy?

39-44
 ABSTRACT:

In this article, we discuss some 'harmless, nonequivalent definitions' each of which is presented in a certain setting and is consistently used throughout the entire discourse, as well as problematic cases that lead to contradictory conclusions. The definitions chosen for this article originated in academic (university and college) calculus sources and on internet sites. We chose prevalent definitions that we considered beneficial in demonstrating the issues at hand. We illustrate our observations by referring to extrema points, inflection points, and monotonicity.