... First, it is clearly not commutative ... That's correct; it's Distributive. We must therefore assume that mathematicians do not f*ck - or more accurately, if they do it does not directly influence the problem at hand. Agree; they are like a few species of fish that both father and mother their offspring. Clearly, it is possible to have a non-integer number of mathematicians; the circumstances are unpleasant to contemplate ... Because all non-integers are irrational numbers. To deal with zero: zero mathematicians can change no lightbulb ... "I can taste no apples" Rene Descartes ... There only remains the problem of boundary conditions. If parallel lines only meet at infinity (not the car), then wouldn't the boundaries be infinite? If so, aren't infinite boundaries a contradiction in terms? Pedantic corrections welcome ... and offered. ... a pastiche of proof instead. Pastiche; is that like panache? How is it served?