I claim to be a Mathematician which means that I get pedantic about use of theorems and definitions, maths should be very precise. Imagine, if you will, my horror as in a computer science lecture a discrete function was differentiated to prove a Theorem. Now I realise it is just a Computer Science lecture, but it had the word "Proof" written above that statement, and it was a mathematical statement, albeit a false one. Now you could claim that its easier to assume that the function is defined on the reals, and then prove it, but I have proved the discrete case and its just as easy. So there really isn't a reason to give untrue proofs.
Rigour people, Rigour.