Cantor Confusion
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From: David Marcus on 19 Nov 2006 20:01 Lester Zick wrote: > On Sat, 18 Nov 2006 13:31:27 -0500, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > >Lester Zick wrote: > >> On Thu, 16 Nov 2006 02:28:14 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > > >> > Are you saying you don't know what the word "proof" means in mathematics? > >> > >> I'm saying you can't prove the truth of whatever you say in or about > >> mathematics. > > > >But, do you know what the word "prove" means in Mathematics? It isn't > >the same as what it means in English. > > Hey gimme a break. I'm still trying to biject the set of {proven} with > the set of {true}. Not happening. I suppose that means you don't know what the word "prove" means in mathematics. I suggest you refrain from responding to any posts that contain the word. > >> >Have you read any math books at the junior/senior college level or > >> >above? > >> > >> Apparently more than you. > > > >Could be. Which math books have you read? > > None. > > >> >What books on the topic have you read? What courses have you taken? > >> > >> Apparently more than you. > > > >Could be. Which books have you read and which courses have you taken? > > None. Ignorance is bliss? I'm not sure how you could have read more books than me if you've read none. -- David Marcus
From: Virgil on 19 Nov 2006 20:17 In article <MPG.1fcaa991fbcf433d989963(a)news.rcn.com>, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > Lester Zick wrote: > > On Sat, 18 Nov 2006 13:31:27 -0500, David Marcus > > <DavidMarcus(a)alumdotmit.edu> wrote: > > >Lester Zick wrote: > > >> On Thu, 16 Nov 2006 02:28:14 -0500, David Marcus > > >> <DavidMarcus(a)alumdotmit.edu> wrote: > > > > > >> > Are you saying you don't know what the word "proof" means in > > >> > mathematics? > > >> > > >> I'm saying you can't prove the truth of whatever you say in or about > > >> mathematics. > > > > > >But, do you know what the word "prove" means in Mathematics? It isn't > > >the same as what it means in English. > > > > Hey gimme a break. I'm still trying to biject the set of {proven} with > > the set of {true}. Not happening. > > I suppose that means you don't know what the word "prove" means in > mathematics. I suggest you refrain from responding to any posts that > contain the word. > > > >> >Have you read any math books at the junior/senior college level or > > >> >above? > > >> > > >> Apparently more than you. > > > > > >Could be. Which math books have you read? > > > > None. > > > > >> >What books on the topic have you read? What courses have you taken? > > >> > > >> Apparently more than you. > > > > > >Could be. Which books have you read and which courses have you taken? > > > > None. > > Ignorance is bliss? > > I'm not sure how you could have read more books than me if you've read > none. Doesn't such a concatenation of claims, having read more books that you and having read none, qualify Zick for a stupid award?
From: David Marcus on 19 Nov 2006 22:13 Virgil wrote: > In article <MPG.1fcaa991fbcf433d989963(a)news.rcn.com>, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > Lester Zick wrote: > > > On Sat, 18 Nov 2006 13:31:27 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > > >Lester Zick wrote: > > > >> On Thu, 16 Nov 2006 02:28:14 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > > > > > > > >> > Are you saying you don't know what the word "proof" means in > > > >> > mathematics? > > > >> > > > >> I'm saying you can't prove the truth of whatever you say in or about > > > >> mathematics. > > > > > > > >But, do you know what the word "prove" means in Mathematics? It isn't > > > >the same as what it means in English. > > > > > > Hey gimme a break. I'm still trying to biject the set of {proven} with > > > the set of {true}. Not happening. > > > > I suppose that means you don't know what the word "prove" means in > > mathematics. I suggest you refrain from responding to any posts that > > contain the word. > > > > > >> >Have you read any math books at the junior/senior college level or > > > >> >above? > > > >> > > > >> Apparently more than you. > > > > > > > >Could be. Which math books have you read? > > > > > > None. > > > > > > >> >What books on the topic have you read? What courses have you taken? > > > >> > > > >> Apparently more than you. > > > > > > > >Could be. Which books have you read and which courses have you taken? > > > > > > None. > > > > Ignorance is bliss? > > > > I'm not sure how you could have read more books than me if you've read > > none. > > Doesn't such a concatenation of claims, having read more books that you > and having read none, qualify Zick for a stupid award? It certainly would seem to meet the minimum qualifications. -- David Marcus
From: imaginatorium on 20 Nov 2006 01:00 Lester Zick wrote: > On Sat, 18 Nov 2006 18:31:05 +0000 (UTC), stephen(a)nomail.com wrote: > > >David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > >> Lester Zick wrote: > >>> On Thu, 16 Nov 2006 02:02:49 -0500, David Marcus > >>> <DavidMarcus(a)alumdotmit.edu> wrote: > >>> >Lester Zick wrote: > >>> >> "Provability" of what pray tell? If you're not concerned with proving > >>> >> the truth of what you say in mathematics exactly when are you not > >>> >> discussing philosophy every time you say anything in mathematics? > >>> > > >>> >Do you really not know the mathematical meaning of the word "prove"? If > >>> >so, I (and others) could try to explain it to you. But, if you are just > >>> >being argumentative, we won't bother. > >>> > >>> What is it you think you're proving? > > > >> Does that mean you don't know the mathematical meaning of the word > >> "prove"? It isn't the same as the English meaning. > > > >>> >Please give a specific example of something that you think is absurd or > >>> >a contradiction. I don't know what you mean by "containment of sets and > >>> >subsets". > >>> > >>> Well as I recollect Stephen seems to think infinite sets are proper > >>> subsets of themselves. > > > >> Are you sure that is what Stephen thinks? > > > >I see Lester has resorted to lying. That was Stephen... I must say I've always been puzzled by accusations of "lying" in this group. In particular, how can a claim to "seem to recollect.." be lying? Of course, one may be annoyed by people who jumble up what one says, but... > Ever since you mathematically demonstrated that dr=v Lester has just > resorted to modern mathematics. That was Lester, with just one of his endearing habits, viz referring to himself in the third person. (Or was that Eldon? Or do all cranks do it?) And of course, another of his endearing habits, viz jumbling up what Stephen said. But when your dog hears "**** ****** **** ******** **** ****** Fido ***** **** ***** dr *** ***** **** **** Fido ****** *** dr ***v *** ****!" how can "woof" be lying? Beats me. > ~v~~ Arf arf! Brian Chandler http://imaginatorium.org
From: mueckenh on 20 Nov 2006 01:36
Virgil schrieb: > > We cannot construct or define or > > recognize a well ordering. > > We can easily define one: any ordering in which every non-empty subset > has a first element. But you cannot define more than countably many. Please lean what "definable well-order" means technically. > > We have no reason to suppose the we could not recognize one if it were > presented for inspection. We cannot recognize it, because it cannot exist. 1) It cannot be defined by a formula. 2) It cannot be listed because of cardinality reasons. 3) It cannot be determined in any other way. (Or do you have an idea?) Hence, we cannot recognize it. > > It is true that no one has actually constructed any explicit well > ordering. > > > It is true that no one will ever have constructed any explicit well ordering. > > > The axiom of infinity does not say anything about ordinal or > > > cardinal numbers. However, given that the set N exists and > > > the defnition of ordinal and cardinal numbers, it is easy to > > > see that if N exists it must have both an ordinal and a cardinal > > > number. > > > > > No. You assume the possibility of a bijection of the set with itself. > > The identity function on any set bijects it with itself. And such > functions are guaranteed, via the axiom of replacement. > > > > That is not proven from the mere existence of the set if we cannot > > recognize or treat all of its elements. > > It is proven in ZF, even without C. The recognizability of all elements is not proven. And it cannot be proven, because we cannot recognize more than countaby mny elements. That is fact, because we cannot denote more elements. But how should we recognize an element which cannot be denoted? I mean, how should anybody except you, be able to achieve that? > > > And even if it had. By means of the equilateral infinite triangle I > > proved that this cannot be the case. Therefore we have a contradiction. > > Since WM assumes properties for his "triangle" which contradict > themselves, as well as contradicting ZF, ZFC and NBG, among others, he > is welcome to all contradictions of his own making, but there are no > other contradictions than those due to his self-contradictory > assumptions. > Among other idiocies, WM keeps claiming that in his triangle there is a > finite line as "long" as the infinite diagonal. Either you are a liar or too stupid to understand. I proved that there is no infinite diagonal. (The diagonal is a subset of the line ends.) Regards, WM |