Young Peoples' Ideas of Infinity

Abstract

This paper considers views of infinity of young people prior to instruction in the methods mathematicians use in dealing with infinity. To avoid overlap with other papers in this special issue on infinity, reference to limit notions and Cantorian views of infinity are kept to the minimum. A partially historical account of studies examining young peoples' ideas of infinity is presented. Methodological problems in accessing such ideas is a sub-theme of this paper. The four main sections deal with: potential pitfalls for research in this area and the work of Piaget; issues concerning the contradictory nature of infinity and infinity as a process and as a object; infinite numbers; contexts and tasks.