THE HOLY GRAIL ~ CANTOR DISPROOF
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From: George Greene on 4 Jun 2010 00:50 On Jun 3, 7:07 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > I think you're a few axioms short of a factual logical system. No, you don't. In the first place, what you are doing has about as much relation to "thinking" as dancing has to architecture. In the second place, logical systems ARE NOT factual, so NObody is thinking about THAT. Logical systems are ABSTRACT. > You need something like, Cretin, PLEASE! You are NOT in ANY position to be telling ANY of US what WE might need! > when categorizing the closure / completeness of a set, Idiot: THERE IS NO SUCH THING as "the closure/completeness of a set". A set is closed (or not) UNDER SOME OPERATION that produces NEW RESULTS from operANDS in the set. If you have the set by ITSELF, witOUT ALSO an operation, THEN YOU CANNOT EVEN SPEAK of closure! Speaking of "closure of a set" as you just have (without clarifying the relevant operation) IS FLAUNTING STUPIDITY! As for completeness, it is NEVER the SET that is complete, BUT RATHER, AGAIN, the set ALONG WITH SOME OPERATION that might be applied to its members. Finally, the "closure/completeness of a set" IS NOT "categorized"!! The set is either closed under the operation or it is not! The operation either produces all of the members of the set (and therefore is, along with whatever it was producing them from, and whatever machinery/framework this was occurring in, complete), OR IT ISN'T! Answering a question yes or no IS NOT "categorizing" anything unless the question was ABOUT categories! > you give a warranty in fine print, an E&OE that states that > self reference and negation of members of the class are omitted. > i.e. extrapolating deductions to infinity are not defined. THIS IS JUST BULLSHIT. The inference rule is called Universal Generalization, it IS well defined, and it "extrapolates" FROM ONE arbitrary constant TO THE WHOLE DOMAIN, BY DEFINITION. THE SIZE OF THE DOMAIN IS *ALWAYS* IMMATERIAL! Whether the domain is or isn't finite NEVER matters! And talking about deductions "to infinity" IS INCOHERENT, almost to the point of being ungrammatical. YOU NEVER SAW ANYONE HERE "extrapolate a deduction to infinity", so whether that is or isn't defined CANNOT EVEN MATTER. What you DID see was people making universal generalization over a domain that might at least possibly be infinite, OR MIGHT NOT. Cantor's theorem DOES NOT require an infinite domain! It is true FOR ALL sets, regardless of size, and the reasoning that proves this IS FINITARY, EVEN when the domain is infinite! > > I think there is a class solution to Russell's Paradox that does something like this. > > e.g. > here is a complete list of subsets of N, barring the list's self reference > and negation that explicitly defeats the closure of the set, however functionally > it has no bearing. > > Otherwise you end up proving that computable reals can't contain > some sequence or another when EVERY DIGIT SEQUENCE TO INFINITE > LENGTH IS IN THE COMPUTABLE LIST OF REALS. > > You can live with that suggestion of a contradiction, apparently you think > 'in the actual infinite expansion' some sequence is missing, but your entire belief > in logic is all about 'dark numbers'. The majority of real numbers that "can't be seen". > > Herc
From: George Greene on 4 Jun 2010 00:51 On Jun 3, 7:07 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > I think there is a class solution to Russell's Paradox that does something like this. No, you don't. Whatever you are doing, it IS NOT THINKing. > > e.g. > here is a complete list of subsets of N, No, here isn't. And there isn't, either, And NOwhere is there "a complete list of susets of N". The problem, of course, is that you don't know what "list" means.
From: George Greene on 4 Jun 2010 00:55 On Jun 3, 7:07 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > Otherwise you end up proving that computable reals can't contain > some sequence or another when EVERY DIGIT SEQUENCE TO INFINITE > LENGTH IS IN THE COMPUTABLE LIST OF REALS. You are LYING. Every digit sequence TO EVERY FINITE length is in the computable list of reals. THERE ARE PLENTY of reals (most of them, in fact) that differ from EVERY computable real at SOME FINITE point in the list! That fact that something holds TO EVERY FINITE position in a list does NOT mean it holds "To infinite" length or "to infinite" position. Your capitalizing it is not going to help. > > You can live with that suggestion of a contradiction, It's ONLY a SUGGESTION, dumbass. It's not AN ACTUAL contradiction. It LOOKS like one TO YOU because YOU'RE STUPID. > apparently you think > 'in the actual infinite expansion' some sequence is missing, We don't just think this. We can prove it. The computable reals CAN BE ENUMERATED, DUMBASS. > but your entire belief > in logic is all about 'dark numbers'. The majority of real numbers that "can't be seen". It is NOT that they can't be SEEN! It is that they ARE INFINITE and so canNOT be SPECIFIED by a FINITE description! If they can't be "seen", then that would not be because they are "dark", but rather because HUMANS only have FINITE eyes and brains! > > Herc
From: Dingo on 4 Jun 2010 00:57 On Thu, 3 Jun 2010 21:55:50 -0700 (PDT), George Greene <greeneg(a)email.unc.edu> wrote: >HUMANS only have FINITE eyes and brains! And Herc has considerably less.....
From: |-|ercules on 4 Jun 2010 01:13
"George Greene" <greeneg(a)email.unc.edu> wrote > On Jun 3, 7:07 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> Otherwise you end up proving that computable reals can't contain >> some sequence or another when EVERY DIGIT SEQUENCE TO INFINITE >> LENGTH IS IN THE COMPUTABLE LIST OF REALS. > > You are LYING. > Every digit sequence TO EVERY FINITE length is in the computable list > of reals. > THERE ARE PLENTY of reals (most of them, in fact) that differ from > EVERY > computable real at SOME FINITE point in the list! Oh boy, what a laugh! You are going to have to pull a big rabbit out of your hat to justify that claim. Which real differs from every computable real at a finite point, and which finite point? The 1000th digit? the 1,000,000th digit? Because every digit sequence is covered up to infinite digits. Or as you put it, every digit sequence is covered up to every (infinite) finite distance. Watch George backpeddle that some uncomputable number differs at a *unknown* finite point in it's expansion, or at an *unspecified* finite point, or *at the end* of the expansion, or *somewhere* on the expansion a digit is different, but it's definitely at a finite digit, the 1st, 2nd, 3rd, maybe the 4th digit is different to every computable. Let's work out what finite digit George found that is DIFFERENT to every computable real. 0.0 is computable 0.1 is computable so it's not the 1st digit. 0.00 is computable 0.01 is computable 0.10 is computable 0.11 is computable so it's not the second digit that. So how long until you find this *finite* positioned digit that is different to every computable real? Herc |