Construction of the final results of infinite iterative processes in individuals’ mind in a geometrical context

Abstract

This study provides a framework for explaining the way individuals might construct the final result of infinite iterative processes in a geometrical context. To this end, 30 undergraduate students were interviewed. The analysis of the data collected yielded two different views: first, there were those who believed that the presented infinite iterative processes will have to end because nothing else could be imagined; second, there were those who claimed that the processes will not end because assuming that a final result will fall out of processes would be paradoxical. In this regard, this study demonstrates how some related paradoxes in a geometrical context can be interpreted, by analyzing their potential sources, within the proposed framework.