"Virgil" <Virgil@home.esc> wrote in message news:Virgil-66F8AC.23332415062010@bignews.usenetmonster.com... > 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.
Well, I am old, and whilst I am familiar with Homer Simpson, I don't know these other two characters.
