THE CANTOR ARGUMENT SO FAR
in [Logic]
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From: |-|ercules on 19 Jun 2010 18:21 ------------------------SCI.MATH----------------------------- Take any list of reals 123 456 789 Diag = 159 AntiDiag = 260 It's a NEW DIGIT SEQUENCE and it works on EVERY LIST. ---------------------------HERC------------------------------ defn(herc_cant_3) The list of computable reals contains every digit (in order) of all possible infinite sequences. ...as a result of containing ALL (infinitely many) finite prefixes. THEREFORE YOU CANNOT CONSTRUCT A NEW DIGIT SEQUENCE --------------------------SCI.MATH-------------------------- BUT: 0.0 0.1 0.2 .... 0.01 0.02 0.03 .... 0.99 0.101 0.102 .... ALSO contains every finite prefix AND 0.111... is not on that list. THEREFORE ANTI-DIAG STILL *IS* A NEW DIGIT SEQUENCE. -----------------------------HERC------------------------------ A correction to a correction does not prove the original assertion. You STILL have not come up with a NEW DIGIT SEQUENCE. You use the term NEW DIGIT SEQUENCE for the finite example 260 then you BAIT AND SWITCH and call it NEW NUMBER because An AD(n) =/= L(n,n). Is it a *NEW DIGIT SEQUENCE* or not? Herc
From: George Greene on 19 Jun 2010 21:24 On Jun 19, 6:21 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > ------------------------SCI.MATH----------------------------- > > Take any list of reals > > 123 > 456 > 789 > > Diag = 159 > AntiDiag = 260 > > It's a NEW DIGIT SEQUENCE and it works on EVERY LIST. It works on every SQUARE list. It obviously won't be a new sequence if the list is LONGER than it is wide (in that case, you just add the constructed anti-diaogonal at the bottom, unless it was already on the list). Your capacity for ALWAYS LYING about what WE (and Cantor) are saying, is, well, breathtaking. > > ---------------------------HERC------------------------------ > > defn(herc_cant_3) > The list of computable reals contains every digit (in order) of all possible infinite sequences. This is STILL MEANINGLESS. YOU CAN'T JUST KEEP SAYING THIS. You DON'T KNOW what CONTAINS means, and even if you did, IT WOULDN'T MATTER. Once again, by YOUR DEFINITION of "contains", THE LIST OF *FINITE* digit-sequences ALSO "contains every digit (in order) of all possible infinite sequences". So UNTIL YOU START OVER, USING THAT list AND NOT "the list of computable reals" (which is a concept FAR BEYOND YOUR understanding, and which list IS NOT, itself, COMPUTABLE), you simply HAVE NOTHING to say.
From: George Greene on 19 Jun 2010 21:27 On Jun 19, 6:21 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > ---------------------------HERC------------------------------ > > defn(herc_cant_3) > The list of computable reals contains every digit (in order) of all possible infinite sequences. > > ..as a result of containing ALL (infinitely many) finite prefixes. > > THEREFORE YOU CANNOT CONSTRUCT A NEW DIGIT SEQUENCE This DOES NOT FOLLOW, DUMBASS! A list that "contains every digit in (in order) of all possible infinite sequences" STILL WILL NOT have SOME reals (MOST reals, in fact, ALWAYS INCLUDING ITS OWN ANTI-DIAGONAL) *ON* it!! Your basic problem, here, in addition to NOT knowing what you mean by "Contains", is that you don't know what you mean BY *New* EITHER! The sequence is NEW (assuming we had a list of everything "old") If And Only If It IS NOT ON the OLD list! The fact that the old list "contained" some sequence does NOT make that sequence "old"! If the sequence was OLD then it WAS ON the list, because the original list was supposed to be the list OF ALL the reals (if it was the list of all computable ones, and if they are all computable, which you are idiotically claiming they are, even though THIS VERY LIST YOU ARE TALKING ABOUT -- this list of all computable reals -- IS ITSELF NOT computable, and that's not even Cantor -- THAT'S TURING -- even if he DID handwave it).
From: George Greene on 19 Jun 2010 21:36 On Jun 19, 6:21 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > ------------------------SCI.MATH----------------------------- > > Take any list of reals > > 123 > 456 > 789 > > Diag = 159 > AntiDiag = 260 Damn, you don't even know how to anti-diagonalize. In an even base, the complement is 1 less than the base, MINUS the number. The "anti"- of d in decimal is 9-d. Usually we do this in binary, where it is 1-b. So the ACTUAL anti-diag here is 840.
From: Mike Terry on 19 Jun 2010 21:49
"|-|ercules" <radgray123(a)yahoo.com> wrote in message news:884u75Fk0aU1(a)mid.individual.net... > ------------------------SCI.MATH----------------------------- > > Take any list of reals > > 123 > 456 > 789 > > Diag = 159 > AntiDiag = 260 > > It's a NEW DIGIT SEQUENCE and it works on EVERY LIST. OK so far... > > ---------------------------HERC------------------------------ > > defn(herc_cant_3) > The list of computable reals contains every digit (in order) of all possible infinite sequences. > Unclear. I'd better rewrite it for you: The list of computable reals contains every finite prefix of all possible infinite sequences. OK ... > ..as a result of containing ALL (infinitely many) finite prefixes. That's what you just said! (Which makes me think maybe you meant something else, but it's unclear what you could mean, and I know you'll never clarify so I won't bother asking...) > > THEREFORE YOU CANNOT CONSTRUCT A NEW DIGIT SEQUENCE FALSE... This doesn't follow from what I've agreed above. But I can correct it again for you: THEREFORE YOU CANNOT CONSTRUCT A NEW FINITE DIGIT PREFIX Now it's OK ... But, this doesn't mean you can't construct a new INFINITE DIGIT SEQUENCE. (As in fact, you obviously can.) Note: "FINITE DIGIT PREFIX" and "INFINITE DIGIT SEQUENCE" have several letters in common, but they are DIFFERENT PHRASES with DIFFERENT MEANINGS. You can't just take a sentence with one phrase and replace it with the other and expect it to remain valid... (That sort of thing is where PROOFs come into the picture. :-) > > > --------------------------SCI.MATH-------------------------- > > BUT: > > 0.0 > 0.1 > 0.2 > ... > 0.01 > 0.02 > 0.03 > ... > 0.99 > 0.101 > 0.102 > ... > > ALSO contains every finite prefix OK... (this is a cleaner list to argue with than above) > > AND 0.111... is not on that list. > Correct... > THEREFORE ANTI-DIAG STILL *IS* A NEW DIGIT SEQUENCE. > You've got it! > > -----------------------------HERC------------------------------ > > A correction to a correction does not prove the original assertion. I haven't a clue what this is referring to. (It sounds impressive though, sort of like "two wrongs don't make a right", or "the inverse of the inverse is the identity".) > > You STILL have not come up with a NEW DIGIT SEQUENCE. 0.111... is not in the list, therefore BY DEFINITION it is a new digit sequence. I'm assuming that given we start with a list of digit sequences, we should count some other digit sequence as "NEW" if it's NOT ONE OF THE ONES WE STARTED WITH? (That seems a natural English language interpretation of new, but if you mean something else, please explain precisely your definition of "new". Hehe.) > > You use the term NEW DIGIT SEQUENCE for the finite example 260 Isn't this your example and your phrase??? Anyway, it seems clear to me that 260 isn't in the original list, so calling it a NEW DIGIT SEQUENCE seems reasonable to me! > then you BAIT AND SWITCH and call it NEW NUMBER because > An AD(n) =/= L(n,n). Do I? I don't even know what that means. I've explained why I would call it a NEW DIGIT SEQUENCE. If we identify DIGIT SEQUENCEs with NUMBERs, then of course 260 is also a NEW NUMBER. > > Is it a *NEW DIGIT SEQUENCE* or not? Um, let's see: EXISTING DIGIT SEQUENCEs: 123 456 789 CANDIDATE DIGIT SEQUENCE: 260 TESTING: 260 = 123 ? <=== No 260 = 456 ? <=== No 260 = 789 ? <=== No RESULT: YES, 260 is a NEW DIGIT SEQUENCE ! ! ! (Duh...) In other words, it not in the list of existing digit sequences, although I think it's likely you're using your own (secret) definition of the phrase NEW DIGIT SEQUENCE. Still, I've explained what *I* mean by the phrase, so at least one of us is being clear... Regards, Mike |