 Suppose M is the set given, and suppose (using Zermelo's notation) that 𝔘M is the set of its subsets (‘Untermengen’). The basic procedure in the 1904 proof was to single out certain subsets of M and to show that these can in effect be ‘chained’ together, starting from modest beginnings (and using the choice function γ); thus we have {m1}, where  m1 = γ(M), {m1, m2}, where again  m1 = γ(M) and  m2 = γ(M − {m1}), and so on. In this way, the proof shows that one can ‘build up’ to the whole of M itself.[28] This ‘build-up’ is one of the things which provoked scepticism, and particularly the step which shows that M itself must be embraced by it. In the 1908 proof, the basic idea is to start from M itself, and consider ‘cutting down’ by the element ‘chosen’ by the choice principle, instead of building up. Thus, if one accepts that if M is a legitimate set, then so is 𝔘M, and there is not the same danger of extending into inconsistent sets, not even the appearance of danger. Again the key thing is to show that the sets defined are in fact ‘chained’ together and are in the right way exhaustive. 