Give me ONE digit position of any real that isn't computable up to that digit position!
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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.
From: |-|ercules on 6 Jun 2010 01:13 "Transfer Principle" <lwalke3(a)lausd.net> wrote .. > 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. It's hard to prove classical mathematics is wrong when every time I dispute your claims you jump back to shore and say "nahh nahh we didn't claim anything factual we just have some axioms and derivations" A proof is essentially a computer program. I'm giving you a description of my 4 algorithms, but you keep asking what syntax and computer I'm using. I'm pointing out your trivial obvious errors, I'm not defining a new branch. But instead off calling you all wrong, I will just say your results are meaningless. Higher infinities and incompleteness and most of your uncomputable claims are just platonic drivel. Mathematics is a machine, so is a turnip incinerator. Herc
From: Transfer Principle on 6 Jun 2010 01:54 On Jun 5, 10:13 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "Transfer Principle" <lwal...(a)lausd.net> wrote .. > > 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. > It's hard to prove classical mathematics is wrong when every time > I dispute your claims you jump back to shore and say "nahh nahh > we didn't claim anything factual we just have some axioms and derivations" What does Herc mean by "factual" here? Does he mean that classical mathematics doesn't prove anything about the real world. If so, then I agree with Herc to some extent. It is true that "ZFC proves that N and R do not have the same cardinality" is indisputable, since it does follow from the axioms of ZFC. Yet one will be hard-pressed to find an uncountable object in the real world. Indeed, some physicists wonder whether length, time, etc., can be quantized (Planck units), which would imply that there's no real-world example of an _infinite_ object, much less an uncountable object. It is precisely for this reason that I am open to reading about alternate theories, as long as those theories don't contradict empirical evidence. Thus, even I won't defend a theory which seeks to prove that 2+2 = 5, since one can prove in the real world that 2+2 = 4, not 5. But since the real world can't prove anything about infinity, I'm open to many different theories about infinity, including NFU, PST (Pocket Set Theory), intuitionism, as well as finitist set theories like ZF-Infinity in which one can't necessarily prove that infinite sets exist. I am even somewhat open to _ultrafinitist_ theories where there's an upper bound on the largest natural number that exists, as long as that upper bound is larger than any number that can describe objects in the real, physical world. > Higher infinities and incompleteness and most of your uncomputable claims are just > platonic drivel. I agree (except for the word "drivel").
From: Marshall on 6 Jun 2010 09:06
On Jun 5, 8:45 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "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. > > 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. For what it's worth: 1) Is uninteresting to me; neither agree nor disagree. 2) The way you phrased it in this post is sorta weird, but in other posts you've said this one says that a computer and a human are on equal footing with regards to Incompleteness; I agree. 3) "disagree" insofar as this one is provably false. 4) Never was clear on what this was claiming. If it's claiming that the real numbers are countable, then disagree. > 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. Disagree. Marshall |