In an algebra course in college we formally rebuilt arithmetic from very basics. We had to define counting number addition in terms of repeated incrementing. Like this in J:
increment =: >: increment 3 4 plus =: increment ^: 3 plus 4 7 And then we went on to define decrement in terms of undoing an increment. decrement =: increment ^:_1 decrement 5 4 Which led to defining subtraction which led to defining zero and negative numbers. And so on for multiplication and division which then led to rational numbers etc. But I think anyone who had to suffer through redefining mathematics formally would appreciate these uses of power. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
