Common Mistakes Due to Mathematical Sophistry

Abstract

Mathematics is present in people's daily lives, whether formally in the school or academic environment, or in places where formalities are not necessarily observed. Using mathematical concepts carelessly can generate results that do not satisfy or do not represent reality. Thus, the objective of this article was to present some sophistry in mathematics, expose some justifications and highlight the errors made in the arguments. From basic expressions, known to a large part of the students, it was demonstrated how to obtain mathematical absurdities. Some resolutions presented were used, generally by students who do not pay attention to the definitions and hypotheses necessary for their correct applications. Also a theorem has been created that affirms the obvious. Thus, it can be concluded that when using invalid mathematical arguments in a demonstration or application, such as those that violate axioms, logical arguments, definitions, or hypotheses, it is possible to deduce contradictions or frightening results, which can bring surprises.

DOI: https://doi.org/10.56238/tfisdwv1-114