The relationship between notions of infinity and strategies used to compare enumerable infinite sets

Abstract

This article aims at examining the relationship between students’ expressed notions of infinity and strategies used to compare the cardinalities of infinite sets. The notions of infinity were classified into two categorizations of potential and actual infinity, and the strategies were classified as part-whole, single infinity, incomparability and one-to-one correspondence. The participants were 104 senior high-school students and the data were collected through a questionnaire consisting of two parts. Analysis of the data showed that, despite the existence of inconsistent responses, there was a significant relationship between the notions of infinity and the strategies used to compare enumerable infinite sets, although the relation was not strong.

KEYWORDS:

• Actual infinity
• comparison of infinite sets
• inconsistency in action
• inconsistency in notion
• potential infinity

Disclosure statement

No potential conflict of interest was reported by the authors.