Work subsequent to 1884 suggests that Cantor felt the need to supply arguments for well-ordering. For instance (Cantor 1895: 493) to show that every infinite set T has a countable subset (and thus that ℵ0 is the smallest cardinality), Cantor set out to prove the existence of a subset of T which is well-ordered like the natural numbers. The key point to observe here is that Cantor felt it necessary to exhibit a well-ordered subset of T, and did not simply proceed by first assuming (by appeal to his ‘Denkgesetz’) that M can be arranged in well-ordered form. He exhibits such a subset in the following way: