Cantor Confusion
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From: David R Tribble on 2 Oct 2006 15:18 Han deBruijn wrote: >> O.K. Call it what you want. But if you and I do not >> agree on what common sense is, I am right. > William Hughes wrote: >> For example: It's common sense that you can't put more >> than an infinite number of balls in a vase. So if you remove >> an infinite number of balls there are no balls left. > Tony Orlow wrote: > Oh. I thought it was common sense that the set of even naturals was > infinite, so if you remove the even naturals from the vase, it would be > empty? What happened to the odd ones? I thought you said that labeling the balls in the vase was irrelevant to the problem and that it was just a parlor trick that set theorists used to impress girls. Are you now saying that the labels might mean something after all?
From: Virgil on 2 Oct 2006 16:18 In article <45216517(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > mueckenh(a)rz.fh-augsburg.de wrote: > > Virgil schrieb: > > > >> In article <1159710911.446611.96530(a)e3g2000cwe.googlegroups.com>, > >> mueckenh(a)rz.fh-augsburg.de wrote: > >> > >>> Dik T. Winter schrieb: > >>> > >>> > >>>> Let's refrase it Cantor's way, please: > >>>> (m, m, m, m, m, ...) > >>>> (w, m, m, m, m, ...) > >>>> (w, w, m, m, m, ...) > >>>> (w, w, w, m, m, ...) > >>>> there is no element of the list that contains w's only. But the > >>>> diagonal constructed contains w's only. > >>> This is the typical one-eyed view of a set theorist. The same we have > >>> with Han's vase: Of course there is no ball which has not jumped out at > >>> noon. We cannot name any such number. But the other eye should see that > >>> there are more balls in than out at any time, including noon. The > >>> refore set theory is useless. One cannot calculate meaningfully with > >>> infinites! > >> One can do some calculations with "infinites" if one is sufficiently > >> careful. > >>> To come back to your argument: The diagonal differs from all the list > >>> numbers at most in one w. > >> That is enough to distinguish between any two successive list members, > >> so is enough to distinguish the "diagonal". > > > > It is enough to distinguish finite numbers, but not to distinguish > > infinite numbers. 1 + n =|= n but 1 + omega = omega. > > > > Regards, WM > > > > IFR distinguishes between a set and itself plus one. IFR at best works for sets having certain kinds of "natural" order relations imposed on them, not on bare sets, nor on sets for which no "natural" order exists.
From: Poker Joker on 2 Oct 2006 19:55 "Virgil" <virgil(a)comcast.net> wrote in message news:virgil-343665.12274830092006(a)comcast.dca.giganews.com... > In article <NNtTg.1856$3E2.504(a)tornado.rdc-kc.rr.com>, > "Poker Joker" <Poker(a)wi.rr.com> wrote: > >> "Virgil" <virgil(a)comcast.net> wrote in message >> news:virgil-988F09.00544830092006(a)comcast.dca.giganews.com... >> >> > It's not what Joker doesn't know that hurts him, its what he knows that >> > ain't so. >> >> Virgil is jealous because he doesn't know anything other than to >> get flame-wars going that allow him to use his talent: acting like >> a three-year-old. > > I might be jealous of someone with some mathematical talent, but not of > someone whose only visible talent is personal attacks. So you are your worst fan.
From: Poker Joker on 2 Oct 2006 19:57 "Virgil" <virgil(a)comcast.net> wrote in message news:virgil-665CA8.12340030092006(a)comcast.dca.giganews.com... > In article <Y3uTg.1861$3E2.1791(a)tornado.rdc-kc.rr.com>, > "Poker Joker" <Poker(a)wi.rr.com> wrote: > >> "Virgil" <virgil(a)comcast.net> wrote in message >> news:virgil-A44A2E.01004230092006(a)comcast.dca.giganews.com... >> > In article <YDmTg.25600$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. >> >> How could you? You've never done any work. > > Never claimed to have done any. But I can and have appreciated the good > work of others, which PJ does not. Virgil is the jerk who admits to doing nothing and yet the NG is riddled with his personal attacks. The archives don't lie.
From: Poker Joker on 2 Oct 2006 20:04
"Dik T. Winter" <Dik.Winter(a)cwi.nl> wrote in message news:J6FJxy.FDu(a)cwi.nl... > In article <YDmTg.25600$QT.1073(a)tornado.rdc-kc.rr.com> "Poker Joker" > <Poker(a)wi.rr.com> writes: > > > > "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. > > No. You are confusing "some list" with "any list". Understandable if you > do not know mathematical terminology. Obviously you are just learning terminology, so to help you, I'm providing a definition of "any" for you. http://dictionary.reference.com/browse/any Example use from the above: "If you have any witnesses, produce them" I produced one. I'm sure you still won't understand. |