"Scott's trick implies that the cardinal number 0 is , which is also the ordinal number 1, and this may be confusing. A possible compromise (to take advantage of the alignment in finite arithmetic while avoiding reliance on the axiom of choice and confusion in infinite arithmetic) is to apply von Neumann assignment to the cardinal numbers of finite sets (those that can be well ordered and are not equipotent to proper subsets) and to use Scott's trick for the cardinal numbers of other sets.[citation needed]
