 In the modern understanding of set theory, to show that there is a well-ordering on M would be to show that there is a set of ordered pairs of members of M which is a relation satisfying the right properties of a well-ordering relation over M. It is well to remember that Zermelo's task in 1908 was constrained in that he had to establish the existence of a well-ordering using only the set-theoretical material available to him. This material did not involve the general notion of ordinal and cardinal numbers, not even the general notions of relation and function. What Zermelo used, therefore, was the particular relation a ⊆ b of being a subset, and it is important to observe that the chain produced is ordered by this relation. 