000135494 001__ 135494
000135494 005__ 20240529145200.0
000135494 0247_ $$2doi$$a10.4102/pythagoras.v45i1.774
000135494 0248_ $$2sideral$$a138652
000135494 037__ $$aART-2024-138652
000135494 041__ $$aeng
000135494 100__ $$0(orcid)0000-0002-7725-3917$$aArnal-Palacián, Mónica$$uUniversidad de Zaragoza
000135494 245__ $$aComparing the finite and infinite limits of sequences and functions: A mathematical and phenomenological analysis and its implications in Spanish textbooks
000135494 260__ $$c2024
000135494 5060_ $$aAccess copy available to the general public$$fUnrestricted
000135494 5203_ $$a The purpose of this article is to conduct a mathematical and phenomenological comparison of three concepts: (1) the finite limit of a function at a point, (2) the finite limit of a sequence, and (3) the infinite limit of a sequence. Additionally, we aim to analyse the presence of these concepts in Spanish textbooks. The methodology employed is exploratory and descriptive. Our mathematical comparison revealed differences in several areas, including the dependence between variables, the involved infinite processes, the types of infinity, the dimensioning for each variable, and the intuition of continuity in the interval. Our phenomenological comparison found a correspondence between phenomena using a formal approach, but differences in phenomena when using an intuitive approach. Finally, our analysis of textbooks revealed that all three limits are most commonly presented in the verbal representation system and definition format.Contribution: This study has contributed to the teaching and learning of the notion of limit.
000135494 536__ $$9info:eu-repo/grantAgreement/ES/DGA/S60-23R
000135494 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000135494 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000135494 700__ $$aClaros-Mellado, Javier
000135494 700__ $$aSánchez-Compaña, María Teresa
000135494 7102_ $$12006$$2200$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Didáctica Matemática
000135494 773__ $$g45, 1 (2024), a774 [8 pp.]$$tPythagoras$$x2223-7895
000135494 8564_ $$s1107492$$uhttps://zaguan.unizar.es/record/135494/files/texto_completo.pdf$$yVersión publicada
000135494 8564_ $$s3035072$$uhttps://zaguan.unizar.es/record/135494/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000135494 909CO $$ooai:zaguan.unizar.es:135494$$particulos$$pdriver
000135494 951__ $$a2024-05-29-14:16:54
000135494 980__ $$aARTICLE