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1 Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia

1 2023

1 Arnal-Palacián M.

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Infinite limit of a function at infinity and its phenomenology

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Arnal-Palacián M.

2023

tom 14

25-41

In this paper we aim to characterise and define the phenomena of the infinite limit of a function at infinity. Based on the intuitive and formal approaches, we obtain as results five phenomena organised by a definition of this limit: intuitive unlimited growth of a function, for plus and minus infinity, and intuitive unlimited decrease of a function, for plus and minus infinity (intuitive approach), and the round-trip phenomenon of infinite limit functions (formal approach). All this is intended to help overcome the difficulties that pre-university students have with the concept of limit, contributing from phenomenology, Advanced and Elementary Mathematical Thinking, and APOS theory. Keywords: limit, infinity, functions, phenomenology, Advanced Mathematical Thinking, APOS