On 2010-06-16, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > All computable, Turing-computable, nonetheless computable, definable > (in any useful, i.e., finite language), and by other means > determinable numbers form a countable set. > > ________________________ > All subsets of N are countable. Big deal. > > If Cantor's diagonal proof results in any such a number, then it > proves in effect the uncountability of a countable set. > > ____________________ > What absolute crap. It proves no such thing. And in any event the diagonal > number is easily computable. Just change all "7"s to "8" and everything else > to "7". Its a few lines of code. > > Otherwise it proves nothing, because an infinite sequence of digits > without other information does not determine anything. > > ____________________ > No, it proves there is a Real which is not on the list.
There is very little in the quoted material to indicate who is saying what. I'm guessing that the sections separated by "____________________" marks are from different posters, but that's about all I can tell. It isn't even clear which sections are newly written by Peter, and which are quotes from earlier conversation (by Peter or someone else).