In a message dated Tue, 15 Oct 2002, Angel Faus writes: > > > Mathematically, 1/0 is not +Infinity. It's undefined/indeterminate > > in the set of rational numbers. The IEEE may say otherwise. > > Mathematically, 1/0 is whatever you define it to be.
Well, sure. That's as axiomatic as saying, "mathematically, the number one is whatever you define it to be." But a mathematical system that has a definition which is inconsistent with the rest of the system is a flawed one. If you let 1/0 be *anything*, then ordinary algebraic logic falls apart. Those silly proofs where it is "proven" that 1 = 2, 1 + 1 = 1, etc., all depend on division by zero being possible (regardless of what its value is). You have to keep division by zero illegal to avoid these absurd results. Hence, to my mind at least, exception-throwing or NaN is a better solution than infinity. But will it really matter one way or the other? Probably not, so we should stop quibbling. Perhaps if someone could demonstrate a real-world need for either NaN or infinity in this case, or else a case for why exception-throwing should *not* go away, we'd be able to bring the discussion somewhere more fruitful. For my part: division by zero is so often a programmer error, and so rarely a useful thing to do, that it seems to me that exception-throwing should remain the behavior in Perl 6. Trey
