Mathematical Imaginings and Pictures

Abstract This paper explores some of the ways that pictures embedded in the prose of mathematics may mislead the mathematician; in particular, the pictures surrounding Cantor's diagonal argument. This work takes up themes from Floyd and Mühlhölzer's recent work and aims to expand upon what it means to be a non‐extensionalist within the context of Cantor's proof. The use of different pictures or conceptions are discussed in relation to Objects of Comparison in Kuusela's sense of the term and are then used to compare the different conceptions of the infinite involved in discussions of the differential calculus on the one hand and of the real numbers on the other, with particular reference to the continuum and the notion of ‘sizes’ of infinity.