In article <627bf325-9dbb-4967-a878-7a0bfd8a4677@s9g2000yqd.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 17 Jun., 09:54, Virgil <Vir...@home.esc> wrote: > > In article <4c19cd2c$0$316$afc38...@news.optusnet.com.au>, > > "Peter Webb" <webbfam...@DIESPAMDIEoptusnet.com.au> wrote: > > > > > Cantor's proof applied to computable numbers proves you cannot form a > > > computable list of computable numbers. Cantor's proof applied to Reals > > > proves you cannot form a computable list of Reals. > > Cantors proof is nonsense from the beginning, because a real number > can never be defined by an infinite sequence alone.
Maybe not to WM, but he is is not GOD to determine what is and what is not true. It is clear that what he thinks is mostly irrelevant here and in mathematics in general.
> A definition > defines something, but an infinite sequence does not define a number > before the last digit is known.
Only such little minds as WM has can argue that an infinite sequence has a last member.
> > > > To be correct, there is no computable list of ALL of the computable > > numbers, even though the set of computable numbers is e countable, but > > there are lots of possible computable lists of computable numbers. > > And there are lots of lists of more than all computable numbers, > namely lists of all finite expressions.
Which statement concedes the existence of infinite lists. Which justifies the "Cantor diagonal" argument.
