Competition, Ordinality, Atomism

Inherent in the concept of Ordinality is continuity between and interdependence of its constituents, i. e. First entails the possibility of Second, Third, etc., while each of its successors presupposes the actuality of at least one predecessor.  So, Atomism, the elements of which are discontinuous and mutually independent, cannot accommodate Ordinality, as preeminent Atomist Russell tacitly concedes when he relies on the ordinal Successor Function to generate Numbers.  Now, sports competition can and often does incorporate Ordinality, e. g. First Place, Second Place, etc., corresponding to which are First Prize, Second Prize., etc.  In contrast, the winner-take-all principle that informs competition in Capitalism reflects the inherently limited Atomist orientation of the system.