On Jan 15, 2008 12:29 AM,
Ben Franksen writes:
jerzy.karczmarczuk@info.unicaen.fr wrote: ...
Does *MATH* answer the question what is: (0/0)==(0/0) ? Nope!
Exactly. So why try to give an answer in Haskell? MATH says: the expression 0/0 is undefined, thus comparing (0/0)==(0/0) is undefined, too. I would expect Haskell to say the same.
I don't know whether you are serious, or you are pulling my leg... Let's suppose that it is serious.
When math says that something is undefined, in my little brain I understand that there is no answer. NO answer.
I'm not sure if I'm agreeing or disagreeing with you here. Depends on exactly what you mean by no answer. When I was a TA for calculus 2, students were presented with something like the following problem: Find the limit: lim (sin x / x) x->0 And proceeding, they would reduce this to: sin 0 / 0 0 / 0 Look in the book that said "0/0 is undefined", and write "undefined" on the paper as if that were the answer. For the calculus uninclined (I figure that is a vast minority on this list), the answer is 1. In that case, undefined meant "you did the problem wrong". And the error was precisely when they wrote 0 on the bottom of the division sign. To me, when math says "undefined"... let me stop there. Math doesn't say "undefined". Instead, when mathematicians say "undefined", they usually mean not that the question has no answer, but that the question you're asking doesn't even make sense as a question. For example, division is only defined when the denominator is not 0. Asking what the answer to "0/0" is is like asking "what happens when I move the king across the board in chess?". That operation doesn't even make sense with those arguments. However, Haskell is not blessed (cursed?) with dependent types, so it is forced to answer such questions even though they don't make sense. But looking to math (at least with a classical interpretation of numbers) is just not going to work. Personally, I loathe the existence of NaN and +-Infinity in floating point types. Someone here made an enlightinging point encouraging us to think of floating point numbers not as numbers but as intervals. That makes me slightly more okay with the infinities, but NaN still bugs me. I'd prefer an error: Haskell's way of saying "you did the problem wrong". That would be most useful in the kinds of things I do with floating point numbers (games). But there are probably other areas where the IEEE semantics are more useful. Well... that paragraph was just a long-winded way of saying "I have an opinion, but I don't think it's very important...". Luke