Cantor Confusion
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From: Poker Joker on 11 Oct 2006 22:41 "Virgil" <virgil(a)comcast.net> wrote in message news:virgil-71ECE1.17260803102006(a)comcast.dca.giganews.com... > 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. Virgil continues to answer posts he knows nothing about. He continues to babble.
From: Poker Joker on 11 Oct 2006 22:42 "Virgil" <virgil(a)comcast.net> wrote in message news:virgil-4B4BA9.17265603102006(a)comcast.dca.giganews.com... > 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. Virgil wishes she could think.
From: Poker Joker on 11 Oct 2006 22:44 "Virgil" <virgil(a)comcast.net> wrote in message news:virgil-DE33FD.21001629092006(a)comcast.dca.giganews.com... > When Joker can prove > "For ANY real number x there is a procedure to find > a real number y, such that x/y=1." > only then need we consider any special cases. Virgil spouts the most asinine things. We all know that there are special cases that have nothing to do with this thread.
From: William Hughes on 11 Oct 2006 22:57 Poker Joker wrote: > "Virgil" <virgil(a)comcast.net> wrote in message > news:virgil-1F12E7.17222503102006(a)comcast.dca.giganews.com... > > 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. > > Virgil is so ignorant that she can't write sentences. You are much better at insulting Virgil than you are at discussing mathematics. You do a lousy job of insulting Virgil. - William Hughes
From: David Marcus on 12 Oct 2006 02:50
Albrecht wrote: > > Virgil schrieb: > > > In article <1160520935.025893.130590(a)h48g2000cwc.googlegroups.com>, > > "Albrecht" <albstorz(a)gmx.de> wrote: > > > > > > > I like to examine the idea of Russell Easterly - building a kind of > > > diagonal number on lists of natural numbers - in respect to this view. > > > First I review his idea: > > > > > > Let's have an arbitrary list of natural numbers: > > > > > > 1: a > > > 2: b > > > 3: c > > > ... > > > > > > with the numbers of digits of the numbers in the list: > > > > > > 1: m > > > 2: n > > > 3: o > > > ... > > > > > > Now we build the "diagonal number" d of the list as follows: > > > > > > We have a look on the first number of the list a which is build out of > > > m digits. We build a number with m+1 digits with the cipher 1. This > > > number is truely greater than a and therefore different from a. > > > It's the first approach to d. (E.g. a = 765 -> m = 3 -> d = 1111) > > > Now we have a look on the second entry of the list. The number b with n > > > digits. If n <= m we let d unchanged. If n > m we build the new number > > > d with n+1 digits, again with the cipher 1. > > > In this way we go through the list. > > > > > > This construction builds up a number d which is different from any > > > number of the list. > > > > > > Unless there is a natural number upper bound on the number of digits > > for numbers in the list, the m,n,o,..., the number of digits in the > > constructed what-ever-it-is will have to be greater than any finite > > number, and thus the constructed whatever-it-is will NOT be a number at > > all. > > But by construction the number must be finite since at every step it is > build up by finite addition to a finite number. When you say "the number", what number are you referring to? In the above construction, it isn't clear that what is constructed will be a natural number. -- David Marcus |