Roger Hui <[email protected]> wrote: > I assume you are talking about mathematical numbers rather than > finite-precision floating point representations of same. In that case, the > first claim (countable number of irrationals can appear as the limit of > computations) is false.
There are only countably many computations -- Godel's correspondence. So there are only countably many irrationals which can be the limit of a computation (that is, a non-terminating computation, such as Chatin's Omega). Chatin proved this result, on the way to proving that the only irrationals which are uncountable are the ones we cannot work with in any way. > The second claim (some pairs of rationals have no > irrationals between them) is false. Good proof, I'm persuaded. -Wm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
