Give me ONE digit position of any real that isn't computable up to that digit position!
in [Math]
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From: Transfer Principle on 5 Jun 2010 23:12 On Jun 5, 2:57 am, Barb Knox <s...(a)sig.below> wrote: > In article > <3fa80824-dca3-4f1d-ba80-9be23eda5...(a)j36g2000prj.googlegroups.com>, > Ostap Bender <ostap_bender_1...(a)hotmail.com> wrote: > > Maybe he is confusing "dark numbers" with "dark matter"? > >http://en.wikipedia.org/wiki/Dark_matter > Unfortunately, the OP is rather in the position of someone today telling > an astronomer that they won't believe in dark matter until someone shows > him some. He wants us to "show" him an uncomputable (i.e. unshowable) > real. ISTM he would be happier if he just concentrated on > intuitionistic or other non-classical systems of mathematics wherein > everything that "exists" is showable, rather than trying to convince all > the rest of us that classical mathematics is "wrong". (And it doesn't > help that his grasp of classical mathematics is rather weak.) 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"? I like to say that if one disagrees with a result that is proved from a theory, it's time to consider a different theory. I hope that Herc will do this, and give us the axioms of his new theory (or "theories").
From: Marshall on 5 Jun 2010 23:20 On Jun 5, 8:12 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > 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"? Neither one. He's using the word "theory" to mean "theorem." What he's trying to do is prove some established theorems false. Marshall
From: Marshall on 5 Jun 2010 23:20 On Jun 5, 8:00 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > On Jun 5, 3:13 am, Ostap Bender <ostap_bender_1...(a)hotmail.com> wrote: > > Of course, this doesn't necessarily mean that Herc has > actually disproved Turing's Halting Theorem in _ZFC_. > > > > Maybe you wouldn't all knock me if some of you ACKNOWLEDGED my theories. > > Ah, _theories_. This seems to indicate that Herc/Cooper > really is discussing more than one theory -- possibly a > theory other than ZFC in which he has actually proved the > negations of statements that are theorems in ZFC. This > would put us in Case 1 of my four-case list. > > If this is the case, then Bender and the others are no > longer justified in criticizing Herc just because he > contradicts standard theory. Very funny. Marshall
From: |-|ercules on 5 Jun 2010 23:45 "Marshall" <marshall.spight(a)gmail.com> wrote.. > On Jun 5, 8:12 pm, Transfer Principle <lwal...(a)lausd.net> wrote: >> >> 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"? > > Neither one. > > He's using the word "theory" to mean "theorem." > What he's trying to do is prove some established > theorems false. Right! 1/ I designed the simplest computer fetch cycle 2/ I proved Godel's proof places no bounds on knowledge 3/ I proved the possible existence of an effective halt algorithm 4/ I showed that higher infinities are thought to be implied by the non existence of a box that contains the numbers of the boxes that don't contain their own number No-one has agreed or disagreed with 1 - 3, a couple have disagreed with 4 without substantiating why. Aatu said they were all wrong then disappeared to work on his *informal proof* of the incontrovertible fact that all informal proofs can be formalized. Herc
From: Transfer Principle on 6 Jun 2010 00:55
On Jun 5, 8:20 pm, Marshall <marshall.spi...(a)gmail.com> wrote: > On Jun 5, 8:12 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > 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"? > Neither one. > He's using the word "theory" to mean "theorem." > What he's trying to do is prove some established > theorems false. Thanks for the clarification. So Herc is trying to prove that established theorems (of ZFC) are false. According to Knox, Herc is trying to prove that classical mathematics is "wrong." And like Knox, I wish that Cooper would just consider an alternate theory (she mentioned intuitionism) if he doesn't like classical mathematics that much. |