Give me ONE digit position of any real that isn't computable up to that digit position!
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From: Jesse F. Hughes on 6 Jun 2010 09:25 Transfer Principle <lwalke3(a)lausd.net> writes: > I agree with Knox, somewhat. I'm grateful that she at > least acknowledges the existence of theories other than > standard/classical ZFC. But, at least according to Herc, > Knox still won't acknowledge Herc's own theory (or > should I say, _theories_, since Cooper used the word in > the plural). > > But this all goes back to the question that I've been > asking this past fortnight or so, ever since Herc > started this recent posting spree. Is Herc really > trying to introduce a new theory (or "theories"), or is > he trying to prove that classical ZFC is "wrong"? What mathematical theory do you think he's "introducing"? Normally, one introduces a theory by specifying it. Herc has offered no axioms at all. I can see no reasonable reading of his posts that suggest he's introducing a theory in the logical sense. His "theory" is that a bunch of theorems is wrong. He has no mathematical theory. -- Jesse F. Hughes "I am the next legend--living, breathing and solving mega problems in the here and now." -- James S. Harris
From: herbzet on 8 Jun 2010 16:03 "Jesse F. Hughes" wrote: > Transfer Principle writes: > > > Also, the mathematician Willard van Orman Quine > > came up with a perfectly respectable theory which > > proves the negation of Cantor's Theorem. Thus, > > according to Bender's logic, Quine must have been > > an anti-Cantor "kook" as well. > > That does not follow. > > Quine produced a coherent, rigorous theory. None of the folks > disputing Cantor's theorem on this newsgroup have done the same. > > Also, Quine did not claim Cantor's theorem was "wrong". Most of the > folks Ostap referred to *do* claim that the theorem is somehow wrong. What would be instructive would be to see at what point in Cantor's proof that |S| < |P(S)| that the proof fails in NF(U). I'm not myself very familiar with NF(U). Or ZF(C) for that matter, ha-ha. -- hz
From: Aatu Koskensilta on 8 Jun 2010 21:37 Marshall <marshall.spight(a)gmail.com> writes: > That's right. Uninteresting. The TM is already too simple to be of > much interest to me. What is done with it could be done with any model > of computation; TMs are adequate for what we do with them but they are > horrifically awful by almost any metric I can think of. They are conceptual simple, a more-or-less straightforward idealised model of the way human computers go about computing stuff, as Turing clearly explains. This is important when discussing, say, the Church-Turing thesis. Other models of computation are better suited for other purposes. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: |-|ercules on 8 Jun 2010 22:26 "Aatu Koskensilta" <aatu.koskensilta(a)uta.fi> wrote > Marshall <marshall.spight(a)gmail.com> writes: > >> That's right. Uninteresting. The TM is already too simple to be of >> much interest to me. What is done with it could be done with any model >> of computation; TMs are adequate for what we do with them but they are >> horrifically awful by almost any metric I can think of. > > They are conceptual simple, a more-or-less straightforward idealised > model of the way human computers go about computing stuff, as Turing > clearly explains. This is important when discussing, say, the > Church-Turing thesis. Other models of computation are better suited for > other purposes. > You're full of sh1t R2. You don't have a frikkin clue what constitutes an important model of computation, obviously. Herc
From: Jesse F. Hughes on 8 Jun 2010 23:55
Transfer Principle <lwalke3(a)lausd.net> writes: > On Jun 7, 4:08 pm, Ostap Bender <ostap_bender_1...(a)hotmail.com> wrote: >> No, what I am saying is that different people have different mental >> abilities. While people with IQs above, say, 95 find Cantor's proof to >> be easy and trivial, others, like yourself, need various props like >> "boxes" to help themselves visualize the diagonalization idea. > > I don't believe that those who reject Cantor's Theorem > must therefore have IQ's under 90 or 95. Ostap didn't say that. -- "Mathematicians are rather important in the infrastructures of many organizations that protect civilization. I've determined that they are a consistent security risk, and seem to have other agendas, other loyalties beyond loyalty to their respective nations." -- James Harris |