Four conceptions of infinity

Abstract

The paper is the result of extensive research carried out among Czech students and focuses on a conception of infinity. The questionnaire survey was taken by 861 students ranging from grades 7 to 13. The aim of the research was to describe the development of students' conceptions of infinity. These conceptions are built on the intuitive phenomenon of the horizon. We monitor the proportional representation of these conceptions in four combinations of views (into the distance and in depth) and contexts (arithmetical and geometrical). It can safely be maintained that the development of the proportional representation of the earliest conception comprehension of the concept of infinity, the so-called natural infinity, is not concurrent with the students' age. The development of the proportional representation of the conception of actual infinity is non-decreasing, at least in the view into the distance, in both contexts with respect to age. In general, it can be stated that the proportional representation of individual conceptions of infinity is strongly dependent on both context and view.

The Set Theory and the Description of Infinity: the Nature of Infinity Perceived from Metaphysics and Ontology

“…Suppose People have two sets, the even numbers, and odd numbers, if People use the structurality to compare the size of two sets, the even numbers will always be bigger than the odd numbers by their cardinality. Because the structurality of natural numbers indicates that for any odd number, there will be an even number following it [9]. However, Dedekind Infinity or set theory infinity explanation for the size of even numbers and odd numbers is they are equal.…”

Pre-Service Science Teachers' Understanding of Infinity Concept: The Case of Image on Convex Lens

“…Infinity in mathematics education: In mathematics education, the concept of infinity is taught especially in advanced mathematics courses such as number theory, analysis and geometry. In these lessons, the concept of infinity is associated with topics such as the classification of numbers, infinite series and limits (Oflaz & Polat, 2022;Krátká, Eisenmann & Cihlář, 2021;Fernández-Plaza & Simpson, 2016;Merand, 2014;Fischbein, Tirosh, & Hess 1979).…”