Brief answer: the author invokes the Axiom of Choice, so the three equations will be really screwball and there will be no way to write them down explicitly. T

Brief answer: the author invokes the Axiom of Choice, so the three equations will be really screwball and there will be no way to write them down explicitly. This is, in some sense, regarded as cheating. (The Axiom of Choice is generally accepted as a legitimate mathematical axiom, but not universally.) http://en.wikipedia.org/wiki/Axiom_of_choice http://en.wikipedia.org/wiki/Axiom_of_choice