Cantor Confusion
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From: Dik T. Winter on 3 Oct 2006 19:22 In article <rOhUg.28090$8_5.9565(a)tornado.rdc-kc.rr.com> "Poker Joker" <Poker(a)wi.rr.com> writes: > "Dik T. Winter" <Dik.Winter(a)cwi.nl> wrote in message > news:J6FJxy.FDu(a)cwi.nl... > > In article <YDmTg.25600$QT.1073(a)tornado.rdc-kc.rr.com> "Poker Joker" > > <Poker(a)wi.rr.com> writes: > > > > > > "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. > > > > No. You are confusing "some list" with "any list". Understandable if you > > do not know mathematical terminology. > > Obviously you are just learning terminology, so to help you, I'm > providing a definition of "any" for you. > > http://dictionary.reference.com/browse/any That is not the *mathematical* definition of "any". -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Virgil on 3 Oct 2006 19:33 In article <v%BUg.32$LU2.25(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "MoeBlee" <jazzmobe(a)hotmail.com> wrote in message > news:1159835574.760854.104260(a)i42g2000cwa.googlegroups.com... > > There is one sentence there that is a question, followed by three > > sentences that are statements. > > Soo you're excuse is that you weren't specific. Now somehow > specifics matter. In general, my post wasn't statements. You > want to claim some special case makes a difference. It was The joker who claimed that a special case could make a difference but was shown to be wrong by Arturo and others.
From: William Hughes on 3 Oct 2006 19:35 Poker Joker 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. That's > why you have no real answer. > Randy Poe wrote three things. 1. I understand that you wrote something. 2. This something didn't make sense 3. This something bears no resemblence to the proof. Which do you disagree with? Note that your statement bears no resemblence to the proof. The proof starts with a list, any list will do. A number is generated. All you need to generate this number is to have a list, so you can generate the number from any list. You cannot assume that the list might be of the type that you cannot generate a number from, because the procedure to generate the number will work on any list. -William Hughes
From: Virgil on 3 Oct 2006 19:37 In article <W%BUg.33$LU2.27(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Virgil" <virgil(a)comcast.net> wrote in message > news:virgil-9DF264.21122402102006(a)comcast.dca.giganews.com... > > In article <85iUg.28307$8_5.15453(a)tornado.rdc-kc.rr.com>, > > "Poker Joker" <Poker(a)wi.rr.com> wrote: > > > >> "MoeBlee" <jazzmobe(a)hotmail.com> wrote in message > >> news:1159814263.984188.257200(a)k70g2000cwa.googlegroups.com... > >> > > >> > Poker Joker wrote: > >> >> I never tried to refute the uncountability of the reals. > >> > > >> > Good. And you've not correctly refuted diagonal arguments that prove > >> > the uncountability of the reals. > >> > > >> >> I don't need to respond to you about Arturo. > >> > > >> > Okay, you don't have such a need. Meanwhile, my point stands that your > >> > original remarks about Arturo's post are incorrect. > >> > >> I asked a question. According to you, the question is incorrect. That's > >> cute. > > > > P.J. asks questions that assume conditions contrary to fact. > > Virgil babbles because he is incapable of understanding. PJ has no specific points on which he can show me wrong so he claims I babble. Whereas I, and others, have show him wrong on specific issues for which his only rebuttal is to claim his critics are babbling. Too weak to be a valid rebuttal, PJ. You will have to try harder.
From: MoeBlee on 3 Oct 2006 19:39
Poker Joker wrote: > "MoeBlee" <jazzmobe(a)hotmail.com> wrote in message > news:1159835574.760854.104260(a)i42g2000cwa.googlegroups.com... > > Poker Joker wrote: > >> I asked a question. According to you, the question is incorrect. That's > >> cute. > > > > You also made a series of statements: > > > > You wrote: > >> "Arturo Magidin" <magidin(a)math.berkeley.edu> wrote in message > >> news:efgfhd$261u$1(a)agate.berkeley.edu... > >> > In article <1159410937.013643.192240(a)h48g2000cwc.googlegroups.com>, > >> > <the_wign(a)yahoo.com> wrote: > >> >>Cantor's proof is one of the most popular topics on this NG. It > >> >>seems that people are confused or uncomfortable with it, so > >> >>I've tried to summarize it to the simplest terms: > >> >> > >> >>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. > >> > > >> > This is hardly the simplest terms. Much simpler is to do a ->direct<- > >> > proof instead of a proof by contradiction. > >> > > >> > 1. Take ANY list of real numbers. > >> > 2. Show that a real can be defined/constructed from that list. > >> > 3. Show that the real from step 2 is not on the list. > >> > 4. Conclude that no list can contain all reals. > >> > > >> > >> How can it be simpler if the list can be ANY list instead of a > >> particular one. ANY list opens up more possiblities than > >> a single list. Also, if its true for ANY list, then it must be > >> true for a specific list. So if considering a single specific list > >> shows a flaw, then looking at ANY (ALL of them) list doesn't > >> help. > > > > There is one sentence there that is a question, followed by three > > sentences that are statements. > > Soo you're excuse is that you weren't specific. I have nothing in this regard that needs excuse. And in earlier posts I addressed the specifics of your misunderstandings. > In general, my post wasn't statements. You > want to claim some special case makes a difference. I didn't say that every sentence in every one of your posts was statement. It was statements that I corrected. MoeBlee |