Cantor Confusion
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From: Poker Joker on 3 Oct 2006 19:06 "Virgil" <virgil(a)comcast.net> wrote in message news:virgil-C78663.21163902102006(a)comcast.dca.giganews.com... > In article <j8iUg.28330$8_5.24730(a)tornado.rdc-kc.rr.com>, > "Poker Joker" <Poker(a)wi.rr.com> wrote: > >> "Virgil" <virgil(a)comcast.net> wrote in message >> news:virgil-B233B9.12324230092006(a)comcast.dca.giganews.com... >> > In article <93uTg.1860$3E2.1673(a)tornado.rdc-kc.rr.com>, >> > "Poker Joker" <Poker(a)wi.rr.com> wrote: >> > >> >> "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. >> > >> > I have, to the satisfaction of anyone competent in mathematics, >> > repeated >> > other's proofs that, despite PJ's objections, no list of reals can >> > contain all reals. >> >> The NG is hardly "anyone competent in mathematics" that's why >> Virgil is so well accepted. > > In addition to the NG, there are all those textbooks and reference works > that agree that the Cantor "diagonal" proof is valid. > > Which is where I found those proofs that P.J. does not accept. Virgil babbles on and on...
From: Poker Joker on 3 Oct 2006 19:09 "Virgil" <virgil(a)comcast.net> wrote in message news:virgil-B9C4DD.12563101102006(a)comcast.dca.giganews.com... > In article <oaPTg.5137$3E2.3874(a)tornado.rdc-kc.rr.com>, > "Poker Joker" <Poker(a)wi.rr.com> wrote: > >> "Randy Poe" <poespam-trap(a)yahoo.com> wrote in message >> news:1159578269.577169.76000(a)m73g2000cwd.googlegroups.com... >> >> >> 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. >> >> So when it's put in extremely simple terms, then you understand >> that the process doesn't always make sense. > > Joker's processes do not make sense to anyone but Joker. > > Which is possibly why he calls himself "Joker". Virgil spends his days babbling.
From: Poker Joker on 3 Oct 2006 19:11 "Randy Poe" <poespam-trap(a)yahoo.com> wrote in message news:1159801355.575790.302710(a)i3g2000cwc.googlegroups.com... > > Poker Joker wrote: >> "Randy Poe" <poespam-trap(a)yahoo.com> wrote in message >> news:1159578269.577169.76000(a)m73g2000cwd.googlegroups.com... >> >> >> 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. >> >> So when it's put in extremely simple terms, then you understand >> that the process doesn't always make sense. > > No, I understand that you wrote something that doesn't > make sense, but that also bears no resemblance to > the proof you're confused about. If you don't understand, then you are confused. That's why you have no real answer. > Nowhere does anybody sane say that there is a digit > which is simultaneously required to have two different > values, in any variant of the Cantor proof (except > yours). Nobody "says" anything in any version.
From: Poker Joker on 3 Oct 2006 19:16 "Dik T. Winter" <Dik.Winter(a)cwi.nl> wrote in message news:J6FIqp.Cr6(a)cwi.nl... > In article <LkiTg.25581$QT.14011(a)tornado.rdc-kc.rr.com> "Poker Joker" > <Poker(a)wi.rr.com> writes: > > "Dik T. Winter" <Dik.Winter(a)cwi.nl> wrote in message > > news:J6CsBJ.Jys(a)cwi.nl... > ... > > > > 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. > > r isn't on any list of reals. Therefore there isn't a complete list of > > reals. > > There is no r that satisfies that condition. That's how the number from step #2 is defined when the input is all the reals. So we conclude that the number from step #2 is ill-defined.
From: Virgil on 3 Oct 2006 19:19
In article <TTBUg.25$LU2.16(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > PJ gets things from Virgil. If he got those things right when he got them, he would be welcome to them. |