Cantor Confusion
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From: Virgil on 30 Sep 2006 02:59 In article <%ymTg.25599$QT.2902(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Alan Morgan" <amorgan(a)xenon.Stanford.EDU> wrote in message > news:efklq5$t5q$1(a)xenon.Stanford.EDU... > > > > But if the construction isn't valid in that special case then it > > isn't valid in the general case either. Thus I *can't* have proven > > it in the general case. That being the case, there should be a flaw > > in the construction in general. Which is.... ? > > Forget about the OP and all other posts and consider your > question. You think that if there is a problem with a special > case, that alone isn't enough for there to be a problem in > general. You want more proof that there is a problem in the > general case. One specific problem isn't good enough for > you to realize that there's a problem? How many problems > does there need to be before there is a problem in general? One for a start. But PJ's argument does not provide even that.
From: Virgil on 30 Sep 2006 03:00 In article <YDmTg.25600$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.
From: Virgil on 30 Sep 2006 03:03 In article <TImTg.25602$QT.20203(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > Virgil *IS* delusional. Argumenta ad hominem reveal the inadequacy of the arguer. > > I love it when mathematicians and Virgil start to act like babies. Argumenta ad hominem reveal the inadequacy of the arguer. >
From: Virgil on 30 Sep 2006 03:06 In article <EKmTg.25603$QT.7112(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Virgil" <virgil(a)comcast.net> wrote in message > news:virgil-B92CDB.20515029092006(a)comcast.dca.giganews.com... > >> By analogy, what you're saying is: > >> > >> For ANY x > >> there is a procedure to find a y such that x/y = 1. > >> > >> Because we are using the verbage "ANY", we don't > >> have to worry about special cases like when x = 0. > >> That's how mathematicians work? > > > > Except that mathematicians can't prove "any" when there are > > counterexamples. And mathematicians can prove "any" in the list of reals > > case. > > You should let mathematicians speak for themselves. They have. I am just citing their statements. > > >> Or are you just saying that you need not look at special > >> cases when we don't want to? Or is it that if a special > >> case is overlooked enough, then it no longer counts? > > > > I am saying that when one can prove something for "any" case then > > special cases are irrelevant. > > Just stick to acting like a three-year-old. You're much better at it. Is that is the best PJ can do? Personal attacks are the last refuge of the incompetent.
From: mueckenh on 30 Sep 2006 05:59
Ross A. Finlayson schrieb: > Remove all the (non-logical) axioms from any theory and then it is the > null axiom theory. If you're interested in a theory that is designed > with the goals of being consistent and complete, I've written some > thousands of pages about it to sci.math. > I am interested here only to show that the list of all lists is countable and has countably many entries. Any list is an entity which requires a finite amount of space dV, be it in the head which thinks of this list or the paper representing it. If the available space V is finite, there is only a finite number of lists V/dV. But if space is infinite, then its infinite diameter can be subdivided in not more than aleph_0 finite intervals. We know in set theory that aleph_0 * aleph_0 * aleph*0 = aleph_0. Therefore we can think of aleph_0 lists with aleph_0 * aleph_0 = aleph_0 entries in the whole space - and not more. Regards, WM |