 Throughout Cantor’s mathematical career he maintained an unwavering, even dogmatic opposition to infinitesimals, attacking the efforts of mathematicians such as du Bois-Reymond and Veronese[36] to formulate rigorous theories of actual infinitesimals. As far as Cantor was concerned, the infinitesimal was beyond the realm of the possible; infinitesimals were no more than “castles in the air, or rather just nonsense” (1893 [1965: 506], translated by Fisher 1981: 118), to be classed “with circular squares and square circles” (1893 [1965: 507], translated by Fisher 1981: 118). His abhorrence of infinitesimals went so deep as to move him to outright vilification, branding them as “Cholera-bacilli of mathematics” (1893 [1965: 505], translated by Fisher 1981: 116). Cantor’s rejection of infinitesimals stemmed from his conviction that his own theory of transfinite ordinal and cardinal numbers exhausted the realm of the numerable, so that no further generalization of the concept of number, in particular any which embraced infinitesimals, was admissible.