 Ernst Zermelo, a crucial figure in our story, said that the theory had historically been “created by Cantor and Dedekind” [Zermelo 1908, 262]. This suggests a good pragmatic criterion: one should start from authors who have significantly influenced the conceptions of Cantor, Dedekind, and Zermelo. For the most part, this is the criterion adopted here. Nevertheless, as every rule calls for an exception, the case of Bolzano is important and instructive, even though Bolzano did not significantly influence later writers.