Googmeister wrote: ) In Turing landmark paper, he was interested in the ) "computable numbers", those real numbers that can be ) approximated to an arbitrary accuracy by a Turing machine. ) ) http://en.wikipedia.org/wiki/Computable_number ) ) This includes all rational and algebraic numbers, and some ) trancendental numbers, including PI. But, there are uncountably ) many real numbers, so most real numbers are not computable.
That's obvious (well, to me it is) but one could say that an uncomputable number is not interesting, because you can't actually name or describe it.
Isn't that in a more general sense why they invented the axiom of choice ? Without that you can't even pick an uncomputable number, I think.
One could argue philosophically that uncomputable numbers don't exist.
SaSW, Willem -- Disclaimer: I am in no way responsible for any of the statements made in the above text. For all I know I might be drugged or something.. No I'm not paranoid. You all think I'm paranoid, don't you ! #EOT