CANTOR DISPROOF <<<<<<<<<<<<<<<<
in [Logic]
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From: |-|ercules on 27 Jun 2010 01:22 "George Greene" <greeneg(a)email.unc.edu> wrote > There IS NOT a computer program that lists the outputs of all computer > programs! > The LIST exists, but howEVER you got it, you DIDN'T get it from a > computer. That is stupid. By the halting theorem no such list exists, it's a hypothetical construct purely to be tested by diagonalization at a conceptual level. It's as real as halt-omega. Mathematicians use the word non-computable for *unknowable* and think they're above the impossibility constraints of algorithms. Herc
From: |-|ercules on 27 Jun 2010 01:32 "George Greene" <greeneg(a)email.unc.edu> wrote : > There IS NOT a computer program that lists the outputs of all computer > programs! WRONG! > The LIST exists, but howEVER you got it, you DIDN'T get it from a > computer. STUPID MISCONCEPTION! The list of computable reals doesn't exist. This is not just a stupid misconception where I thought George was referring to a list of computable reals existing. George is just wrong. It's trivial to multitask every input to every Turing Machine such that every given finite index of TM and input will give an output should an output exist. Herc
From: Sylvia Else on 27 Jun 2010 01:40 On 27/06/2010 1:20 PM, |-|ercules wrote: > "Sylvia Else" <sylvia(a)not.here.invalid> wrote... >> On 27/06/2010 12:56 PM, |-|ercules wrote: >>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote ... >>>> On 27/06/2010 8:06 AM, |-|ercules wrote: >>>>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>>>>> On 26/06/2010 8:45 PM, |-|ercules wrote: >>>>>>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>>>>>>> On 26/06/2010 3:40 AM, Graham Cooper wrote: >>>>>>>>> On Jun 25, 8:23 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: >>>>>>>>>> On 25/06/2010 7:07 PM, Graham Cooper wrote: >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>>> On Jun 25, 6:54 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: >>>>>>>>>>>> OK. >>>>>>>>>> >>>>>>>>>>>> "1 start with an infinite list of all computable reals". >>>>>>>>>> >>>>>>>>>>>> That is any list of all the computable reals, howsoever >>>>>>>>>>>> constructed. >>>>>>>>>> >>>>>>>>>>>> "2 let w = the maximum width of complete permutation sets" >>>>>>>>>> >>>>>>>>>>>> Where a complete permutation set is all the possible >>>>>>>>>>>> combinations of >>>>>>>>>>>> some finite number of digits. So this step doesn't involve >>>>>>>>>>>> doing >>>>>>>>>>>> anything with the list described in step 1? It's a completely >>>>>>>>>>>> independent step? >>>>>>>>>> >>>>>>>>>>>> Sylvia. >>>>>>>>>> >>>>>>>>>>> Hmmm. Did you consider that the CPS found in the list of >>>>>>>>>>> step 1 was what I meant. Step 1 - consider this list... >>>>>>>>>> >>>>>>>>>> I'm reluctant to assume you mean anything unless it's stated. It >>>>>>>>>> seems >>>>>>>>>> to cause difficulties. However, apparently CPS is an >>>>>>>>>> abbreviation for >>>>>>>>>> "complete permutation set". >>>>>>>>>> >>>>>>>>>> So the list of all computable reals contains as a subset complete >>>>>>>>>> permutation sets whose width is unbounded. Slightly rewording 2, >>>>>>>>>> gives us: >>>>>>>>>> >>>>>>>>>> "2 let w = the maximum width of those complete permutation sets" >>>>>>>>>> >>>>>>>>>> and the next step is >>>>>>>>>> >>>>>>>>>> "3 contradict 2" >>>>>>>>>> >>>>>>>>>> How is it to be contradicted? >>>>>>>>>> >>>>>>>>>> Sylvia. >>>>>>>>> >>>>>>>>> There is no (finite) maximum. >>>>>>>> >>>>>>>> So there is no finite maximum. How does that advance your proof? >>>>>>> >>>>>>> >>>>>>> There seems to be 2 possibilities. >>>>>>> >>>>>>> 1 All finite digit permutations occur to infinite length. >>>>>> >>>>>> It's certainly true that any digit permutation of finite length will >>>>>> be on the list, but that's not a proof that all infinite sequences >>>>>> are >>>>>> on the list. >>>>>> >>>>>> Certainly some infinite sequences are on the list, because they are >>>>>> computable, but you haven't proved that all infinite sequences are on >>>>>> the list. >>>>>> >>>>>>> >>>>>>> 2 It would be very difficult to come up with a new sequence of >>>>>>> digits >>>>>>> that wasn't on the computable reals list >>>>>> >>>>>> The anti-diagonal wouldn't be on it. Now, you might feel that the >>>>>> anti-diagonal is obviously computable, in that each digit can be >>>>>> obtained algorithmically from the list. But that presupposed that a >>>>>> list of computable reals is itself computable, which you haven't >>>>>> proved. We know that it is countable, but that's not the same thing. >>>>>> >>>>>> Sylvia. >>>>> >>>>> >>>>> You assumed the 'finite sequences only' analogy to my proof to >>>>> claim 1. >>>>> >>>>> Then you used 1 to imply 2, using the result of the diagonal attack to >>>>> discredit my attack >>>>> of the diagonal attack. >>>>> >>>>> Herc >>>> >>>> The anti-diagonal is merely an example of a number that isn't on the >>>> list. Leave out my comment about the anti-diagonal, and go back a >>>> moment. >>>> >>>> "1 All finite digit permutations occur to infinite length." >>>> >>>> What exactly does this mean? It doesn't prove that all infinite >>>> sequences are present. >>> >>> True, this is your claim of the proof. >> >> I'm not even sure what that means. >> >> Herc, you're the person presenting the proof. You have to prove each >> step. You can't just assert things and expect people to accept them. >> >>> >>> >>>> >>>> "2. It would be very difficult to come up with a new sequence of digits >>>> that wasn't on the computable reals list." >>>> >>>> It might well be very difficult. But so what? Very difficult isn't the >>>> same as impossible. >>>> >>> >>> >>> Your construction technique is very simple, but considering every object >>> referred to that >>> I put into words is misinterpreted wherever possible, every little thing >>> I write has >>> to be 100% explicit with no other possible bindings or connotations to >>> any terms, even if I refer >>> to something in the same sentence as "it", or the previous sentence says >>> 'regarding this' >>> or the thread topic is X, you all interpret everything as Y, every other >>> possible object under the sun is given priority over what I'm referring >>> to, so I from now on I will not write 'very difficult' when I mean >>> impossible. I think I actually have made a mistake, I thought I was >>> talking to >>> people not robots who need single interpretation only explicit comments >>> because their contextual >>> disambiguator circuitry has blown a fuse. >> >> If you meant impossible, then the problem with 2 is that you haven't >> proved it. > > > I just told you in the other thread, your opinion is moot. You aren't > qualified and > you have demonstrated confusion over numerous points that everyone else > already knows. > > Stop trolling my proof thread with "THIS ISN'T PROOF" dozens of times. > > If you think my induction only works on finite prefixes and not over > entire infinite expansions > then YOU prove that assertion. > Consider the following proposition: For any *finite* list of infinite digit sequences, one can use the anti-diagonal method to produce a sequence that is not in the list. Do you have any difficulty with that? Sylvia.
From: |-|ercules on 27 Jun 2010 02:34 "Sylvia Else" <sylvia(a)not.here.invalid> wrote >> If you think my induction only works on finite prefixes and not over >> entire infinite expansions >> then YOU prove that assertion. >> > > Consider the following proposition: > > For any *finite* list of infinite digit sequences, one can use the > anti-diagonal method to produce a sequence that is not in the list. > > Do you have any difficulty with that? No. This is precisely my point. 123 456 789 Diag = 159 Anti-Diag = 260 260 is a NEW DIGIT SEQUENCE. Add in.... the box of box numbers that doesn't contain such and such box numbers, the halt-omega non computable real, the finite prefixes list not implying any infinite sequence exists, 0.3, 0.33, 0.333, ... not containing 1/3, ZFC defining an antidiagonal, and it's no wonder you want to believe! It's like a big jigsaw puzzle that fits together and forms the concept TRANSFINITE, all you have to do is refute counterclaims by picking an argument at random! Herc
From: Sylvia Else on 27 Jun 2010 03:33
On 27/06/2010 4:34 PM, |-|ercules wrote: > "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>> If you think my induction only works on finite prefixes and not over >>> entire infinite expansions >>> then YOU prove that assertion. >>> >> >> Consider the following proposition: >> >> For any *finite* list of infinite digit sequences, one can use the >> anti-diagonal method to produce a sequence that is not in the list. >> >> Do you have any difficulty with that? > > No. This is precisely my point. > > 123 > 456 > 789 > > Diag = 159 > Anti-Diag = 260 > > 260 is a NEW DIGIT SEQUENCE. > OK, so you accept that it is true for any finite list. That is, that for any finite list there is a sequence that is not in the list, or to put it another way, all finite lists omit at least one sequence. Note that the requirement that the length of the list be finite doesn't impose any maximum on the length. By analogy with your argument that extrapolates from a list that contains all finite permutations to a list that contains all infinite sequences, I'll argue that by extroplating from the fact that all finite lists omit at least one sequence one can conclude that an infinite list omits at least one sequence. The latter of course contradicts your thesis, but either extrapolating from the finite to the infinite is valid, or it isn't. Without some demonstration that the circumstances are materially different, you can't argue that the extrapolation is valid in one case, and invalid in the other. Sylvia. |