Omega Position – a specific phase of perceiving the notion of infinity

Abstract

This article describes a specific phase of the ontogenetic development of understanding infinity, called the omega position, the identification of which is one of the results of extensive research focusing on the perception of the infinity notion. Some 1 432 Czech pupils and students between the ages of 8 to 20, participated in the first two sections of this research between the years 2008 and 2011. This article describes in more detail, the final qualitative part of the research that focuses on interviews with university students with the aim of diagnosing this phase in their perception of infinity in various contexts. It also describes some possibilities for the identification of the omega position and its consequences for a successful study of those notions and ideas of mathematics, which are associated with infinity. Further, the article puts the omega position into context with potential or actual infinity, specifies individual developmental phases by means of the notion horizon and explains some possibilities for mutual interference in the abovementioned developmental phases, employing the following two notions: that of primary and secondary intuition.