Exploring conceptions of infinity via super-tasks: A case of Thomson’s Lamp and Green Alien

• Removed totality from the abstract.
• Our focus is on the influence of context rather than a change of context.
• Further clarification of research methods.
• Reducing abstraction is our main theoretical framework.
• The “existence of totality” is not investigated.

In mathematics education research paradoxes of infinity have been used in the investigation of conceptions of infinity of different populations, including elementary school students and pre-service high school teachers. In this study the Thomson’s Lamp paradox and a variation of it, the Green Alien, are used to investigate the naïve and emerging conceptions of infinity in a group of liberal arts university students, and the effect of context on such conceptions. We describe the difficulties that students face and the strategies they employ to make sense of the counterintuitive situations. This study contributes to research on the use of paradoxes in mathematics education and to research on understanding infinity, with a focus on infinitely small quantities.