Why can no one in sci.math understand my simple point?
in [Logic]
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From: Virgil on 15 Jun 2010 17:03 In article <69655163-949d-4a90-a867-ce409f3b258f(a)c33g2000yqm.googlegroups.com>, WM <mueckenh(a)rz.fh-augsburg.de> wrote: > On 15 Jun., 16:23, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > > "Peter Webb" <webbfam...(a)DIESPAMDIEoptusnet.com.au> writes: > > > So (B) is equivalent to the statement "there exists an uncomputable > > > number". > > > > Right. But why then did you say the number was computable? > > And in what form does it exist? If WM did say it was computable, then it either exists as a computable number of WM is wrong again.
From: Virgil on 15 Jun 2010 17:07 In article <ee9de39b-0511-4088-a62a-2febd5424b43(a)c10g2000yqi.googlegroups.com>, WM <mueckenh(a)rz.fh-augsburg.de> wrote: > On 15 Jun., 16:32, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > > WM says... > > > > > > > > >On 15 Jun., 12:39, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > > > > >> That's *all* that matters, for Cantor's theorem. The claim > > >> is that for every list of reals, there is another real > > >> that does not appear on the list. > > > > >The claim is only proved for every finite subset of the list. > > > > The proof does not make use of any property of infinite lists. > > The proof establishes: (If r_n is the list of reals, and > > d is the antidiagonal) > > > > forall n, d is not equal to r_n > > As every n is finite, it belongs to a finite initial segment of the > infinite list. By WM's argument, proofs by induction are all invalid. So that I, for one, will choose to reject WM's argument rather than rejecting inductive proofs. > > > > There is no "extrapolation" involved. The way that you prove > > a fact about all n is this: > > > > Prove it about an unspecified n. > > Specified or not. n is finite anyhow and belongs to a finite initial > segment of the list. Only for that always finite segment the proof is > correct. By WM's argument, proofs by induction are all invalid. So that I, for one, will choose to reject WM's argument rather than rejecting inductive proofs.
From: Jesse F. Hughes on 15 Jun 2010 17:02 Transfer Principle <lwalke3(a)lausd.net> writes: > On Jun 14, 9:13 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> There's no need for bullying (George), it's just a maths theory. >> Address the statements and questions and add your own. > > I want to avoid using five-letter insults in a thread unless > another poster in the thread has introduced that word. > > Here, Herc calls George Greene a "bully." > > Now whether Greene deserves to be called "bully" is open to > a debate, but still, there must be an underlying reason that > posters like Herc and galathaea use the word "bully" to > describe posters like Greene. > > I see that WM has joined this thread as well. Normally, I > would be grateful to see Cooper and WM work together to stand > up to the "bully" Greene -- except I noticed that Greene has > yet to post in this thread or respond to Herc at all. > > Also, in this thread, WM calls Jesse Hughes a "crank," and > then Daryl McCullough argues that the word "crank" more > accurately describes WM than Hughes. > > I agree with McCullough to some extent. Based on his posting > habits, Hughes is more likely to agree with posters who merit > the "bully" label than those who merit the "crank" label. > > But, as I mentioned earlier, I will not divide posters into > group, but let other posters group for themselves. And so if > WM believes that "crank" is the grouping label that best > describes Hughes, than who am I to interfere with that? I wonder why you think these comments should matter to anyone? So WM calls me a crank. Big deal. So, in your odd view of fairness, you refuse to call me a crank or bully, but rather simply comment that others could call me either. Yeah. Okay. Thanks ever so much for this penetrating analysis. You are indeed the Howard Cosell of sci.math. -- "That's all the legacy I ever wanted, to have people remember me like a shooting star streaking across their Life sky, illuminating, for just one moment, unparalleled beauty unique to itself." -- Weblogs are a particularly humble medium, unique to themselves.
From: Aatu Koskensilta on 15 Jun 2010 17:07 Virgil <Virgil(a)home.esc> writes: > For any undecidable proposition ,P, the number defined by "if P then x > else y", where x and y are computable numbers and not equal, defines > an uncomputable number. No it doesn't. Computability is a purely extensional notion. In addition, there is no mathematical definition of undecidability (of propositions) in any absolute sense. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Jesse F. Hughes on 15 Jun 2010 17:15
stevendaryl3016(a)yahoo.com (Daryl McCullough) writes: > WM says... >> >>On 15 Jun., 18:57, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: >> >>> >>> >We should not use oracles in mathematics. >>> >>> On the contrary! Many real numbers in physics are not computable >>> to infinite precision (for example, the fine structure constant). >> >>Numbers are computable. The fine structure constant is a name. It has >>soem 20 letters. > > I can see that you don't understand the distinction between > use and mention. "Daryl" is a name having five letters. Daryl > is a human being. Hey, "Daryl" *does* have five letters. That makes Daryl a five letter insult, right? (Stop looking at me like that.) -- Jesse F. Hughes "He was still there, shiny and blue green and full of sin." -- Philip Marlowe stalks a bluebottle fly in Raymond Chandler's /The Little Sister/ |