Chuck Simmons wrote: >>>>(a + 1)(a - 1) = (a - 1) (factor it) >>>>(a + 1) = 1 (cancel common factors) >>>> >>If a is one as you said in the other post, (a-1) is zero and thus you'll >>be dividing the expression by zero which is not allowed. >>See link in my other post for more info. >> > > Just be very watchfull of division by zero. IEEE floating point always > allows it because it makes sense. If a is not zero, a/0 is plus or minus > infinity depending on the sign of a. If a is zero, a/0 is NAN. As it > happens, these rules and a few others, though seeming silly, save hours > in screwing around with exception handling in numerical analysis. > Another good feature of IEEE floating point is it allows floating > underflow which is another condition that makes sense (VAX floating > point made floating underflow an error - a grievous architectural > blunder which I never understood).
That would be the real numbers two-point completion (danish: fuldstændiggørelse). Believe me, this is *not* a simpler numberspace to equation solving in. Now you have to watch additions and subtraction as well as division and multiplication when doing calculations, as these are no longer injective. E.g., if \infty is +infinity and -\infty is minus infinity, and a,b is reel numbers then: a/0=b/0 if a has the same sign as b. However, sometimes it is a simpler numberspace to state theorems in. Also, as you state yourself, numerical analysis is sometimes simpler in this space. regards, Esben
