 But for some infinite sets (notably the set of all integers, including the negative numbers, and also the set of rational numbers) there is no first element under their standard ordering. In this case, it is possible to re-order the elements of the set so that every non-empty subset has a first element, so that this process works. Such an ordering is called a well-ordering. (That every set can be well-ordered is, as Zermelo famously proved in 1904, equivalent to the Axiom of Choice.)