> On Feb 5, 10:50 am, "T.H. Ray" <thray...@aol.com> > wrote: > > > Speaking only for my own characterization, I find > no > > conflict between the set theoretic definition and > > mine. > > What was your particular characterization again? If > it's not > extensional then it's in conflict with the set > theoretic definition. > It's both extensional and intensional--though incomplete, as I pointed out--to define function as the transformation of one set of numbers to another. The property of relation inheres in every function.
> In ordinary mathematics, one may be called to prove > that something > (call it 'C') is or is not a function, and the way to > do that is show > that C is or is not a relation such that for all x, > y, z, if <x y> and > <x z> in C, then y=z. On the other hand, with these > various informal > definitions, what even IS the mathematical (and > compatible with > classial mathematics, as that is the context of the > ordinary > mathematics a sixth-grader will go on to study in > college) means that > one would prove that something is or is not a > function? > Sure. See my explanation to Ostap Bender as to why his description that assigns properties is not a function, absent a relation between sets.