[Haskell-cafe] Re: Why does the class called "Real" support only rationals, and not all reals?

Yes, I'm afraid that you are understanding correctly. Annoying isn't it. It is well-known (among Haskell mathematicians at least) that the numeric type classes in the prelude are broken. Here's one proposal for a small step in the right direction: http://hackage.haskell.org/trac/haskell-prime/ticket/112 But it really needs a mathematician to sit down and sort it out properly.