 Frege mercilessly exposes the inadequacies of Heine and Thomae’s position‐their confusions as they slip from term to game formalism; their conflation of sign and signified; the fact that they do not set out an account of the syntax and proof theory which is remotely adequate as an account of the mathematics with which they deal; their hopeless attempts to extend their position from arithmetic to treat of analysis and real numbers, by this stage in mathematical history construed by Weierstrass, Cantor and others not geometrically but as infinite sequences. Thus Frege writes: