My FINAL Cantor thread!
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From: Transfer Principle on 26 Jun 2010 01:16 On Jun 25, 10:08 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "Mike Terry" <news.dead.person.sto...(a)darjeeling.plus.com> wrote > > In any case, the list does not have any *uncomputable* reals in it, and > > these are of "width" omega (first infinite ordinal). So (4) above is still > > correct, and your w does not exist. OR... maybe you have a secret proof > > that *all* infinite digit sequences are computable? > I'm glad for the open mindedness of your final statement, because the top down attacks > on my proof are merely blind belief that ZFC is complete. ZFC isn't complete. There are many statements phi such that ZFC proves neither phi nor ~phi. The most well-known example is the Continuum Hypothesis.
From: |-|ercules on 26 Jun 2010 01:20 "Transfer Principle" <lwalke3(a)lausd.net> wrote .. > On Jun 25, 10:08 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> "Mike Terry" <news.dead.person.sto...(a)darjeeling.plus.com> wrote >> > In any case, the list does not have any *uncomputable* reals in it, and >> > these are of "width" omega (first infinite ordinal). So (4) above is still >> > correct, and your w does not exist. OR... maybe you have a secret proof >> > that *all* infinite digit sequences are computable? >> I'm glad for the open mindedness of your final statement, because the top down attacks >> on my proof are merely blind belief that ZFC is complete. > > ZFC isn't complete. There are many statements phi such that > ZFC proves neither phi nor ~phi. The most well-known > example is the Continuum Hypothesis. I mean *finished* to the extent that it produces true formula. Herc
From: |-|ercules on 26 Jun 2010 03:21 "|-|ercules" <radgray123(a)yahoo.com> wrote > 006666666.. > 016666666.. > 106666666.. > 116666666.. > > The structure of the first 2 digits is a complete permutation set. this is trivially false as I switched from binary to decimal in my reasoning. Herc
From: George Greene on 26 Jun 2010 12:39 On Jun 26, 1:18 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > I don't believe you're that stupid you can't follow was w is. > Mike gets it, Sylvia half gets it, but you don't. Go figure! I assure you, THEY DON'T get it. You have fun playing with others here to and only to the extent that they are closer to being AS STUPID AS YOU ARE. More to the point, since YOU are the one who doesn't get it, it DOES NOT EVEN MATTER what Max or Sylvia get! The question is, will they ever have any success in pulling YOU up to their level? > Maybe the max width IN the set would be easier for you? Two points (which is one too many for you, but they both matter): 1) IN MATH, WE USE QUANTIFIERS to do this. THEN, THERE IS NO confusion. But this would require you TO ACTUALLY LEARN something. It would require you to STUDY some NEW LANGUAGE that is not the muddle in which you normally talk. NO, we are NOT holding our breath. 2) The width IS NOT IN the set: the widths are widths OF ELEMENTS in, of INDIVIDUAL REAL numbers in, the set. A width CANNOT BE IN a set! THE ONLY things that can be IN a set (of reals) ARE REALS! These reals can (and must, and do) HAVE widths! If the set is the set of ALL finite sequences of digits then THERE IS NO MAXIMUM width of <the reals in the set>! You might want to say the maximum is "infinity", but THERE ARE NO infinitely wide sequences in a set of all and only FINITE sequences, SO THAT'S NOT RIGHT EITHER! > > And its the width of the Complete Permutation Set not the reals themselves, > whoops, I mean the width of the initial permuations IN the CPS! > > Herc
From: George Greene on 26 Jun 2010 12:44
On Jun 26, 1:18 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > And its the width of the Complete Permutation Set THERE IS NO SUCH THING as "the complete permutation set"! WHY do you think you can keep using the word "permutation"?? No permutations are relevant here. You have not even clarified whether you are "permuting" horizontally or vertically. If you are permuting "horizontally" then it does NOT MATTER; the result of permuting the digits in ONE real IS JUST ANOTHER REAL. If the first real was computable and the permutation was computable then the resulting real WILL ALSO BE COMPUTABLE and was therefore ALREADY ON your list! You ARE NOT ADDING anything by talking about permutations! > not the reals themselves, A permutation of a real IS a real (unless you permute some of the numbers to be infinitely far from the start, which is not possible if you were doing it with transpositions), so THIS IS A MEANINGLESS distinction! People who are letting you continue to use "permutation" are just adding complexity for you to get lost in. > whoops, I mean the width of the initial permuations IN the CPS! If the original list is a list of computable reals then, yes, "the width" is appropriate BECAUSE THEY ALL HAVE THE EXACT SAME (infinite) width. There is in that case NO question about any "max". The max is only relevant if INSTEAD of using the list of computable reals, you use the list of FINITE digit-sequences. BOTH of these have the property that they match ANY real (computable OR NOT) up to ANY (and EVERY) finite width, so I don't see why it is so important to you to use the computable list, or to start talking about irrelevant permutations of it. No matter how you permute the list OF ALL AND ONLY the computable reals, it is STILL a list of all and only the computable reals. IT DOES NOT MAKE ANY DIFFERENCE whether you do or don't permute it. Different permutations will give you different anti- diagonals, but that just means you are MORE WRONG -- there are MORE numbers that CAN'T be on the list! |