In article <4c1841c6$0$17174$afc38c87@news.optusnet.com.au>, "Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> wrote:
> "Virgil" <Virgil@home.esc> wrote in message > news:Virgil-966F99.20493515062010@bignews.usenetmonster.com... > > In article <4c181d87$0$17178$afc38c87@news.optusnet.com.au>, > > "Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > > > >> > Nevertheless your "definition" belongs to a countable set, hence it is > >> > no example to save Cantors "proof". > >> > > >> > Either all entries of the lines of the list are defined and the > >> > diagonal is defined (in the same language) too. > >> > >> Yes. If you provide a list of Reals, then the diagonal is computable and > >> does not appear on the list. > >> > >> > Then the proof shows > >> > that the countable set of defined reals is uncountable. > >> > >> No, it shows that all "definable" (computable) Reals cannot be explicitly > >> listed. This is *not* the same as being uncountable. > >> > >> > >> > Or it does not > >> > show anything at all. > >> > > >> > >> It shows that all "definable" (computable) Reals cannot be explicitly > >> listed. This is a well known proof in set theory. This is *not* the same > >> as > >> being uncountable. > >> > >> > >> > To switch "languages" is the most lame argument one could think of. > >> > The diagonal argument does not switch languages. And it cannot be > >> > applied at all because the list of all finite defiitions does not > >> > contain infinite entries. Those however are required for the diagonal > >> > argument. > >> > > >> > >> No, that paragraph above is close to gibberish. Cantor said and proved > >> that > >> any purported list of all Reals cannot contain all Reals. His proof is > >> simple and clear, provides an explicit construction of at least one > >> missing > >> Real, and does contain or require any concepts of uncomputable numbers, > >> or > >> use of the Axiom of Choice. > > > > Isn't there a missing "not" in that last sentence between "does" and > > "contain"? > > Oops.
When I was younger, one excused such thing by saying "Even Homer nods", but the young today don't seem to know about the Iliad and Odyssey.
