Possibility to Algorithmically Check: Yet Another Reason Why Current Definitions Have Been Selected in Elementary Mathematics

Authors

Christian Servin, El Paso Community CollegeFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

11-2020

Comments

Technical Report: UTEP-CS-20-112

Published in Applied Mathematical Sciences, 2020, Vol. 14, No. 18, pp. 881-886.

Abstract

At first glance, many definitions in mathematics -- especially in elementary mathematics -- seem arbitrary. Why is 1 not considered a prime number? Why is a square considered to be a particular case of a parallelogram -- in some old textbooks, a parallelogram was defined in such a way as to exclude the square. In his 2018 article, Art Duval explained many such definitions by a natural requirement to make the corresponding results (theorems) as simple as possible. However, elementary mathematics is not just about theorems and proofs, it is also about computations. In this paper, we show that from the computational viewpoint, it is also preferable, e.g., to view a square as a particular case of a parallelogram.