135494 20260219090929.0 doi 10.4102/pythagoras.v45i1.774 sideral 138652 ART-2024-138652 eng Arnal-Palacián, Mónica Universidad de Zaragoza (orcid)0000-0002-7725-3917 Comparing the finite and infinite limits of sequences and functions: A mathematical and phenomenological analysis and its implications in Spanish textbooks 2024 Access copy available to the general public Unrestricted  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. info:eu-repo/grantAgreement/ES/DGA/S60-23R info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es 0.7 2024 0.236 2024 Education 2024 Q3 Mathematics (miscellaneous) 2024 Q4 1.2 2024 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Claros-Mellado, Javier Sánchez-Compaña, María Teresa 2006 200 Universidad de Zaragoza Dpto. Matemáticas Área Didáctica Matemática 45, 1 (2024), a774 [8 pp.] Pythagoras 2223-7895 1107492 http://zaguan.unizar.es/record/135494/files/texto_completo.pdf Versión publicada 3035072 http://zaguan.unizar.es/record/135494/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:135494 articulos driver 2026-02-19-09:00:06 ARTICLE