Cantor Confusion
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From: Poker Joker on 3 Oct 2006 18:59 "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.
From: Poker Joker on 3 Oct 2006 18:59 "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.
From: Poker Joker on 3 Oct 2006 19:03 "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. Now somehow specifics matter. In general, my post wasn't statements. You want to claim some special case makes a difference.
From: Poker Joker on 3 Oct 2006 19:04 "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.
From: Poker Joker on 3 Oct 2006 19:05
"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. |