Cantor Confusion
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From: Virgil on 3 Oct 2006 19:20 In article <CUBUg.26$LU2.22(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Virgil" <virgil(a)comcast.net> wrote in message > news:virgil-52B960.20492402102006(a)comcast.dca.giganews.com... > > In article <CHhUg.27967$8_5.24503(a)tornado.rdc-kc.rr.com>, > > "Poker Joker" <Poker(a)wi.rr.com> wrote: > > > >> "Virgil" <virgil(a)comcast.net> wrote in message > >> news:virgil-665CA8.12340030092006(a)comcast.dca.giganews.com... > >> > In article <Y3uTg.1861$3E2.1791(a)tornado.rdc-kc.rr.com>, > >> > "Poker Joker" <Poker(a)wi.rr.com> wrote: > >> > > >> >> "Virgil" <virgil(a)comcast.net> wrote in message > >> >> news:virgil-A44A2E.01004230092006(a)comcast.dca.giganews.com... > >> >> > In article <YDmTg.25600$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. > >> > > >> > Never claimed to have done any. But I can and have appreciated the good > >> > work of others, which PJ does not. > >> > >> Virgil is the jerk who admits to doing nothing > > > > That I do not claim to have done anything does not imply that I have not > > done anything. > > > > That PJ does not understand that is a mark of his own arrogance. > > Virgil proves PJ's case. PJ hasn't got a case, except possibly of his empties.
From: Virgil on 3 Oct 2006 19:22 In article <TVBUg.27$LU2.7(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Virgil" <virgil(a)comcast.net> wrote in message > news:virgil-C9AC49.20550702102006(a)comcast.dca.giganews.com... > > >>I'm sure you still won't understand. > > > > The context of "list" in which "any list" occured required such lists > > to be functions from the naturals to the reals, which The Poker's > > pseudolists are not. > > > > Ergo, the Poker is committing the fallacy of the straw man, which echos > > the contents of his head quite well. > > Virgil obviously can't understand. No one need even try to understand what contains as little sense as PJ's claims.
From: Poker Joker on 3 Oct 2006 19:24 "William Hughes" <wpihughes(a)hotmail.com> wrote in message news:1159714452.259786.215790(a)b28g2000cwb.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 the sentence above makes no sense. The sentence > above has nothing to do with the proof. > > Diagonal process. > > We make a number > d by specifying every one the digits > in a decimal expansion. > > for every n > > find the real number r=f(n) > > express r in decimal notation (note this won't > work if you express r in binary notation. Soluiton. > Don't do that!) > > find the n'th decimal digit of r, If > this is 5 set d_n to 4. Otherwise set > d_n to 5. > > The only assumption made is that f(n) is a real number > for every natural number n (i.e. that we have a list). > Even if (contrary to fact) we assume the list contains all > real numbers we can still find d. (Since we made an > assumption contrary to fact this will lead to a contradiction. > This is of course the whole point!) > > Assume that the list contains all real numbers. > Make d as above (note there is no step you > cannot do). Since the list contains all > real numbers d must be in the list. Let d = f(m) > Then the mth digit of d must be both 4 and 5. > Contradiction. > > Note that we create d first and find the > contradiction second. We do not start > with a contradiction. f(m) is the mth real. What does d have to do with it? d is the output of a seperate process, isn't it? R is the image of f(m). d = PROCESS( f( n : n in N ) ) so d = PROCESS(R). if d in R then d is self-referential and therefore meaningless.
From: Virgil on 3 Oct 2006 19:26 In article <2XBUg.29$LU2.9(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Virgil" <virgil(a)comcast.net> wrote in message > news:virgil-7521E3.21035802102006(a)comcast.dca.giganews.com... > > In article <aVhUg.28212$8_5.23558(a)tornado.rdc-kc.rr.com>, > > "Poker Joker" <Poker(a)wi.rr.com> wrote: > > > >> "Tonico" <Tonicopm(a)yahoo.com> wrote in message > >> news:1159644048.194388.236080(a)e3g2000cwe.googlegroups.com... > >> > Poker Joker wrote: > >> > > >> > ........nonsenses and rather weird attacks...... > >> > > >> > > >> >> So you think a process that takes all reals can produce one that isn't > >> >> in the set of all reals is possible? > >> > > >> > No, I don't...do you? And what process are you talking about? So far > >> > you've only mentioned the rather huge nonsensical mumbo-jumbo "if a > >> > list [sic] contains all the reals then trying to build a real that is > >> > not there...blah-blah"... > >> > >> If you can't understand that's not my problem. > > > > But that P.J. does not understand, as is the case, is his problem. > >> > >> > .And if the natural number 4 were a multiple > >> > of 3 then Moscow would be Rwanda's capital city: from a false statement > >> > ANYTHING can be deduced. What? That there can be a list [sic] > >> > containing all the reals? Prove it. I can prove, mathematically and not > >> > with ranting, that it can't be so > >> > >> You obviously don't understand the discussion. > > > > But that P.J. does not understand, as is the case, is his problem. > >> > >> > >> >> Wait, I get it. You want to use the consequences of having such > >> >> a process to prove that there is such a process. Now I understand > >> >> your logic. > >> > > >> > Well, it's refreshing to know you're understanding something at least > >> > and at last, even if it is something produced by your own imagination. > >> > >> Like I said, you obviously don't understand the discussion. > > > > But that P.J. does not understand, as is the case, is his problem. > > > > Of one proves that there is a method independent of the list of reals it > > is applied to that will produce a real not in that list, then there is > > no point in assuming anything that contradicts that proof. > > > > But that P.J. does not understand, as is the case, is his problem. > > Virgil answers to posts he knows nothing about. He continues to babble. As PJ is babbler in chief, he continues to do more of it than anyone else, just to maintain his position.
From: Virgil on 3 Oct 2006 19:26
In article <OXBUg.30$LU2.7(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Virgil" <virgil(a)comcast.net> wrote in message > news:virgil-96EEEB.21091902102006(a)comcast.dca.giganews.com... > > In article <l1iUg.28279$8_5.20941(a)tornado.rdc-kc.rr.com>, > > "Poker Joker" <Poker(a)wi.rr.com> wrote: > > > >> "Arturo Magidin" <magidin(a)math.berkeley.edu> wrote in message > >> news:efp1lh$25uv$1(a)agate.berkeley.edu... > >> > In article <LWOTg.5030$3E2.3848(a)tornado.rdc-kc.rr.com>, > >> > Poker Joker <Poker(a)wi.rr.com> wrote: > >> >> > >> >>"Arturo Magidin" <magidin(a)math.berkeley.edu> wrote in message > >> >>news:efmf1m$c88$1(a)agate.berkeley.edu... > >> >> > >> >>>>So if considering a single specific list > >> >>>>shows a flaw, then looking at ANY (ALL of them) list doesn't > >> >>>>help. > >> >> > >> >>> .. since no flaw has been exhibited by looking at any specific > >> >>> list (and "specific" in this case must mean explicit and specific, > >> >>> not > >> >>> a putative list with putative properties whose existence cannot be > >> >>> established a priori; otherwise, we might just say "take a list for > >> >>> which the argument does not work", which is of course nonsense), > >> >>> discussions about this are a waste of time. > >> >> > >> >>First you obfuscate the discussion by saying that specific cases > >> >>don't matter. > >> > > >> > No. FIRST, I presented a proof that holds for an arbitrary list. Then > >> > YOU obfuscated the matter by pretending your own shortcomings in > >> > understanding basic mathematical terminology somehow invalidates that > >> > proof. > >> > > >> >> Now you seem to imply they do, > >> > > >> > Still your own shortcomings being projected. > >> > > >> > If you have a proof that holds for an arbitrary list, in which the > >> > ONLY property of the list being used is the fact that it is a list, > >> > then consideration of particular specific cases is immaterial. You are > >> > free to check particular specific cases if it helps in YOUR > >> > understanding (or lack thereof) of the proof. > >> > > >> > If you can somehow exhibit a specific (explicit) instance in which the > >> > argument does not hold, then you would have shown that what was > >> > presented was an invalid argument. But in order to do so, one must > >> > exhibit a specific COUNTEREXAMPLE. > >> > > >> > In the case of a "proof" that attempted to show that for every real > >> > number x there exists a real number y such that x*y = 1, you would > >> > exhibit > >> > x=0, run through the proof (perhaps) and point out exactly which step > >> > is invalid with that specific number. That's fine. > >> > > >> > On the other hand, if we had a proof that for every real number x > >> > there exists a real number y such that x+y = 0, then a "particular > >> > case" would not be "let x be some real number, which might or might > >> > exist, which has no additive inverse; then your proof is wrong because > >> > your proof would imply it has, contradicting the fact that x does not > >> > have an additive inverse." At that point, your "particular case" is > >> > nothing but hot air and irrelevancy. > >> > > >> >> but in this discussion > >> >>they still don't because of the obfustated argument that somehow > >> >>they don't. > >> >> > >> >>After all, you never showed how step #2 isn't self-referential > >> > > >> > After all, you never showed you understood what step 2 really was; > >> > your claims that it was "self-referential" were hollow and as such > >> > they need not be addressed. The burden of proof is on you, since I > >> > have discharged mine by offering a valid proof. > >> > >> I see no proof here. > > > > That P.J. does not see something is hardly evidence that it is not there > > to be seem, particularly with P.J.'s blatant record of seeing what is > > not and not seeing what is. > > > > > > > > > >> What am I to make of your statement that you did? > >> You are not sincere. > > > > A good deal more sincere that P.J. > > > >> You make all sorts of claims. You back it with nothing. > > > > P.J., on the other hand backs his claims with less than nothing, at > > least by the standards he applies to Arturo. > > > > > >> > No doubt, your understanding of that is about as accurate as your > >> > understanding of Cantor's proof or of mathematical arguments in > >> > general. I wouldn't try to borrow against its value. > >> > >> I understand it much better than you think. > > > > All the evidence P.J. presents contradicts that claim. > > Virgil babbles all over the NGs. If that is the worst PJ can think up to say, he is slipping. |