On the classic paradox of infinity and a related function

Author:

Wijeratne Chanakya1,Zazkis Rina2

Affiliation:

1. Department of Mathematics, University of Colombo, Colombo 00700, Sri Lanka

2. Faculty of Education, Simon Fraser University, Burnaby, BC V5A 1S6, CANADA

Abstract

Abstract In this study we consider a classic paradox of infinity and its variations and suggest how the sources of misleading intuition can be analysed using the concept of uniform convergence of functions. We then examine how six mathematics honour students engage with a variation of the paradox. Despite their advanced mathematical training, the participants experienced considerable difficulty in addressing the presented paradoxical situation. Drawing on data from written responses and individual interviews, we describe the students’ approaches in an attempt to reconcile their intuitive perceptions with their mathematical computations.

Publisher

Oxford University Press (OUP)

Subject

Education,General Mathematics

Reference18 articles.

1. The intuition of infinity;Fischbein;Educ. Stud. Math.,1979

2. The evolution with age of probabilistic, intuitively based misconceptions;Fischbein;J. Res. Math. Educ.,1997

3. Limits;Cornu,1991

4. Epistemology of visual thinking in elementary real analysis;Giaquinto;Br. J. Philos. Sci.,1994

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