Cantor Confusion
in [Math]
|
Prev: Pi berechnen: Ramanujan oder BBP
Next: Group Theory
From: Virgil on 2 Oct 2006 23:03 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.
From: Virgil on 2 Oct 2006 23:09 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.
From: Dik T. Winter on 2 Oct 2006 23:03 In article <virgil-B07103.13122701102006(a)comcast.dca.giganews.com> Virgil <virgil(a)comcast.net> writes: > In article <1159710187.186119.102420(a)i3g2000cwc.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: .... > > By forcing it can be proved that, even including AC, the reals cannot > > be well ordered. > > That is not in accord with the following: > http://en.wikipedia.org/wiki/ZFC#The_axioms > Axiom of choice: For any set X there is a binary relation R which > well-orders X. This means that R is a linear order on X and every > nonempty subset of X has an element which is minimal under R. Mueckenheim is talking nonsense. To quote: <http://mathworld.wolfram.com/AxiomofChoice.html>, "In Zermelo-Fraenkel set theory (in the form omitting the axiom of choice), Zorn's lemma, the trichotomy law, and the well ordering principle are equivalent to the axiom of choice (Mendelson 1997, p. 275)." Forcing did show that he axiom of choice and the continuum hypothesis are independent of each other in ZF theory. -- 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 2 Oct 2006 23:12 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.
From: Virgil on 2 Oct 2006 23:13
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. |