Cantor Confusion
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From: Virgil on 30 Sep 2006 14:26 In article <1159620019.413262.312370(a)i3g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > In article <451dddd9(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > > > > > > > > > > > > The original proof was regarding a complete language using > > > at least two symbols, m and w, no? > > > > Not quite. Two disjoint sets of synbols. > > > > > That was later conflated to a proof about the reals. > > > > It was later shown that it could be modified to form a proof that the > > set of all reals is uncountable. > > This was *not* "later shown", but at the very time of publishing in > 1890/91 Cantor considered this very proof as the proof of the > uncountability of he reals. > > Cantor, in the first paragraph: " Es l??t sich aber von jenem Satze > [uncountability of the reals] ein viel einfacherer Beweis liefern, der > unabh?ngig von der Betrachtung der Irrationalzahlen ist." > My translation: "Here is a much simpler proof of the theorem > [uncountability of the reals] which is independent of the reference to > irrational numbers" As it is not clear that this sentence refers to any such theorem, I take leave to doubt "Mueckenh"'s claim.
From: Virgil on 30 Sep 2006 14:27 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.
From: Virgil on 30 Sep 2006 14:29 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.
From: Virgil on 30 Sep 2006 14:32 In article <93uTg.1860$3E2.1673(a)tornado.rdc-kc.rr.com>, "Poker Joker" <Poker(a)wi.rr.com> wrote: > "Virgil" <virgil(a)comcast.net> wrote in message > news:virgil-4F0272.01064530092006(a)comcast.dca.giganews.com... > > > Is that is the best PJ can do? Personal attacks are the last refuge of > > the incompetent. > > That's been your ONLY attack. I have, to the satisfaction of anyone competent in mathematics, repeated other's proofs that, despite PJ's objections, no list of reals can contain all reals. That "attack" on PJ's position suffices for anyone whose opinion I value.
From: Virgil on 30 Sep 2006 14:34
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. |