Cantor Confusion
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From: Poker Joker on 30 Sep 2006 08:54 "Virgil" <virgil(a)comcast.net> wrote in message news:virgil-988F09.00544830092006(a)comcast.dca.giganews.com... > It's not what Joker doesn't know that hurts him, its what he knows that > ain't so. Virgil is jealous because he doesn't know anything other than to get flame-wars going that allow him to use his talent: acting like a three-year-old.
From: Randy Poe on 30 Sep 2006 09:03 Tony Orlow wrote: > Randy Poe wrote: > > Poker Joker wrote: > >> "Dik T. Winter" <Dik.Winter(a)cwi.nl> wrote in message > >> news:J6CsBJ.Jys(a)cwi.nl... > >>> In article <070Tg.14143$8_5.3402(a)tornado.rdc-kc.rr.com> "Poker Joker" > >>> <Poker(a)wi.rr.com> writes: > >>>> "Randy Poe" <poespam-trap(a)yahoo.com> wrote in message > >>>> news:1159494111.724651.95600(a)i3g2000cwc.googlegroups.com... > >>>> > >>>>> That's incorrect. You don't have to assume none map onto R in order to > >>>>> prove none map onto R. > >>>>> > >>>>> The direct argument starts this way: Let f be any such function, from > >>>>> naturals to reals. > >>>> Certainly we should assume that f *MIGHT* have R as its image, right? > >>> You may assume that, but that assumption is not needed. > >> Certainly not for ostriches. > >> > >>>>> Now, are you saying that somehow that misses some possible functions > >>>>> from naturals to reals? How so? > >>>> No, but we haven't proven that the image of f can't be R in step #1, > >>>> right? > >>>> So step #2 isn't valid, right? > >>> Remember: > >>>> 1. Assume there is a list containing all the reals. > >>>> 2. Show that a real can be defined/constructed from that list. > >>>> 3. Show why the real from step 2 is not on the list. > >>>> 4. Conclude that the premise is wrong because of the contradiction. > >>> Why is step 2 invalid? > >> Do you always accept steps that have questionable validity? > > > > Why does step 2 have "questionable validity"? > > > >>>> Under the most general assumption, we can't count out that > >>>> R is f's image, so defining a real in terms of the image of > >>>> f *MIGHT* be self-referential, and it certainly is if the image > >>>> of f is R. > >>> What is the problem here? > >> I assume you accept this proof that there are no complete lists > >> of reals: > >> > >> Let r be a real number between 0 and 1. Let r_n denote the nth digit > >> in r's decimal expansion. Let r_n = 5 if r_n = 4, otherwise let r_n = 4. > > > > That doesn't make sense. You are saying that every digit of r > > both is equal to 4 and is equal to 5. > > > > Consider r = 0.00000000... > > > > So you're saying the first digit of r is 4 because the first digit of > > r isn't 4? What the hell are you talking about? > > Duh. Sounds like PJ's constructing an anti-diagonal. > > > > >> r isn't on any list of reals. Therefore there isn't a complete list of > >> reals. > > > > That bears no resemblance at all to a proof. > > > > - Randy > > > > It bears much resemblance to Cantor's second regarding uncountability > of...a set. The original proof was regarding a complete language using > at least two symbols, m and w, no? Why don't you sketch this resemblance in detail. In particular, the part that says that any symbol that equals m equals w, and any symbol that equals w equals m, OK? - Randy
From: Poker Joker on 30 Sep 2006 09:12 "Virgil" <virgil(a)comcast.net> wrote in message news:virgil-663D2E.01034230092006(a)comcast.dca.giganews.com... > Argumenta ad hominem reveal the inadequacy of the arguer. You've proven that time and again.
From: Poker Joker on 30 Sep 2006 09:12 "Virgil" <virgil(a)comcast.net> wrote in message news:virgil-4F0272.01064530092006(a)comcast.dca.giganews.com... > Is that is the best PJ can do? Personal attacks are the last refuge of > the incompetent. That's been your ONLY attack.
From: Poker Joker on 30 Sep 2006 09:13
"Virgil" <virgil(a)comcast.net> wrote in message news:virgil-A44A2E.01004230092006(a)comcast.dca.giganews.com... > In article <YDmTg.25600$QT.1073(a)tornado.rdc-kc.rr.com>, > "Poker Joker" <Poker(a)wi.rr.com> wrote: > >> "Virgil" <virgil(a)comcast.net> wrote in message >> news:virgil-9C1609.21071129092006(a)comcast.dca.giganews.com... >> >> > It is in mathematics. Once a proof for any list is established, it >> > covers every list. >> >> This list doesn't contain 4: >> >> 1 >> 2 >> 3 >> >> Proof: >> >> The 1st number isn't 4. >> The 2nd number isn't 4. >> The 3rd number isn't 4. >> That list does't contain 4 >> >> Therefore, Virgil believes that in mathematics, no >> list contains 4. > > As it is PJ's proof, it must be PJ's theorem. > I lay no claim to other's works. How could you? You've never done any work. |