Cantor Confusion
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From: Virgil on 3 Oct 2006 19:39 In article <_0CUg.34$LU2.17(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Virgil" <virgil(a)comcast.net> wrote in message > news:virgil-0F6EAB.21135602102006(a)comcast.dca.giganews.com... > > In article <p6iUg.28316$8_5.5972(a)tornado.rdc-kc.rr.com>, > > "Poker Joker" <Poker(a)wi.rr.com> wrote: > > > >> "Virgil" <virgil(a)comcast.net> wrote in message > >> news:virgil-799E10.12290030092006(a)comcast.dca.giganews.com... > >> > In article <E2uTg.1859$3E2.1096(a)tornado.rdc-kc.rr.com>, > >> > "Poker Joker" <Poker(a)wi.rr.com> wrote: > >> > > >> >> "Virgil" <virgil(a)comcast.net> wrote in message > >> >> news:virgil-663D2E.01034230092006(a)comcast.dca.giganews.com... > >> >> > >> >> > Argumenta ad hominem reveal the inadequacy of the arguer. > >> >> > >> >> You've proven that time and again. > >> > > >> > Glad PJ has finally admitted his sins. > >> > >> You mean the terrible thoughts I have about your abilities > >> being limited to acting like a three-year-old? > > > > P.J. speaks like the two year old he mentally resembles. > > Virgil's babbling is quite boring. He isn't even creative > in his babbling. PJ's babbling about babbling is even more boring. If PJ cannot find any valid arguments against all those proofs of his wrongheadedness, he would make less of a fool of himself by being silent.
From: Virgil on 3 Oct 2006 19:42 In article <w1CUg.35$LU2.8(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "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$3E2.1673(a)tornado.rdc-kc.rr.com>, > >> > "Poker Joker" <Poker(a)wi.rr.com> wrote: > >> > > >> >> "Virgil" <virgil(a)comcast.net> wrote in message > >> >> news:virgil-4F0272.01064530092006(a)comcast.dca.giganews.com... > >> >> > >> >> > Is that is the best PJ can do? Personal attacks are the last refuge > >> >> > of > >> >> > the incompetent. > >> >> > >> >> That's been your ONLY attack. > >> > > >> > I have, to the satisfaction of anyone competent in mathematics, > >> > repeated > >> > other's proofs that, despite PJ's objections, no list of reals can > >> > contain all reals. > >> > >> The NG is hardly "anyone competent in mathematics" that's why > >> Virgil is so well accepted. > > > > In addition to the NG, there are all those textbooks and reference works > > that agree that the Cantor "diagonal" proof is valid. > > > > Which is where I found those proofs that P.J. does not accept. > > Virgil babbles on and on... Apparently PJ's eyes have gone bad and he can no longer make out my words. Get somebody to read them to you. PJ. And get them to read you a few works on logic and mathematics into the bargain. Your ignorance is, at least theoretically, curable.
From: William Hughes on 3 Oct 2006 19:48 Poker Joker wrote: > "Dik T. Winter" <Dik.Winter(a)cwi.nl> wrote in message > news:J6FIqp.Cr6(a)cwi.nl... > > In article <LkiTg.25581$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. If the input is a list the number from step #2 is defined. Your problem is that you are not satisfied with any set of real numbers that is the image of a function defined on the naturals. You want to be able to say - a list for which step #2 is not defined but you cannot. To say a list for which step #2 is not defined is not enough. you have to find a specific list for which step #2 is not defined. This cannot be done. It is easy to see that step #2 is defined for any list. You want to be able to say - a list which contains all real numbers. but we do not know whether such a list exists. We do know that for ANY list we choose step #2 is defined. -William Hughes
From: Virgil on 3 Oct 2006 19:54 In article <J4CUg.36$LU2.19(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Virgil" <virgil(a)comcast.net> wrote in message > news:virgil-B9C4DD.12563101102006(a)comcast.dca.giganews.com... > > In article <oaPTg.5137$3E2.3874(a)tornado.rdc-kc.rr.com>, > > "Poker Joker" <Poker(a)wi.rr.com> wrote: > > > >> "Randy Poe" <poespam-trap(a)yahoo.com> wrote in message > >> news:1159578269.577169.76000(a)m73g2000cwd.googlegroups.com... > >> > >> >> Let r be a real number between 0 and 1. Let r_n denote the nth digit > >> >> in r's decimal expansion. Let r_n = 5 if r_n = 4, otherwise let r_n = > >> >> 4. > >> > > >> > That doesn't make sense. You are saying that every digit of r > >> > both is equal to 4 and is equal to 5. > >> > >> So when it's put in extremely simple terms, then you understand > >> that the process doesn't always make sense. > > > > Joker's processes do not make sense to anyone but Joker. > > > > Which is possibly why he calls himself "Joker". > > Virgil spends his days babbling. PJ has a very limited vocabulary. Which matches his limited mathematical and logical comprehension. Which is why he was so wrong.
From: Virgil on 3 Oct 2006 19:58
In article <Y6CUg.37$LU2.2(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: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. He understands that PJ is confused. > That's why you have no real answer. That's why PJ cannot speak to the specifics of the "diagonal" construction. > > > 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. A lot of people have described the construction required in the "diagonal" proof quite adequately. If PJ does not get it, the fault is his, not theirs. |