On studying equivalent (or not) definitions; the case of limits in R and R2

• Autores: Joanna Mamona-Downs
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 55, Nº. 5, 2024, págs. 1243-1255
• Idioma: inglés
• DOI: 10.1080/0020739X.2022.2053755
• Texto completo no disponible (Saber más ...)
• Resumen

  • This paper initiates a teaching sequence that focuses on building up equivalent definitions to the standard ones for the limit concept in Real Analysis. It comprises two parts: The first provides a classroom assignment where students, guided by Analysis lecturers, are led to develop an alternative definition to the ϵ−δ one for limits of one-variable real functions that are based on the realisation of the interval of δ’s. In the second one, students are directed by their instructor to restore equivalence between two distinct definitions of limit for a function mapping a subset of R2 into R. This is done by adding a condition to one of the definitions, resulting in a third definition that is equivalent to the other one.