Symbolic representations of infinity: the impact of notation and numerical syntax

Past research indicates that concepts of infinity are not fully understood. In countably infinite sets, infinity is presumed to be perceived as larger than any finite natural number. This study explored whether symbolic representations of infinity are processed as such through contrasts with Arabic and verbal written numbers. Comparisons between the infinity word and number words were responded to faster than comparisons of two number words, but not when the infinity symbol was solely compared to Arabic numbers. Moreover, infinity comparisons yielded distance-like effects, suggesting that infinity (both word and symbol) can be misconceived as a “natural number” closer to larger numbers than small ones. These findings demonstrate difficulty perceiving the physically smallest stimulus (∞) as the upper end-value and seem to reflect a limited understanding of symbolic forms of infinity among adults. They further highlight the impact of notation and numerical syntax on how we process symbolic numerical information.