My FINAL Cantor thread!
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From: |-|ercules on 26 Jun 2010 01:08 "Mike Terry" <news.dead.person.stones(a)darjeeling.plus.com> wrote >> > should imply there is unlimited width of all sequences. >> >> Aaaargh, now you've gone back to unclear mode. What does "unlimited width >> of all sequences" mean? >> >> Whatever it means, it obviously does not imply all (countably) infinite >> permutations are in the list, because that's obviously false. (Not even 1 >> infinite digit permuatation is in the list :-) > the proof is lost on you. I will say again I am not building infinite amount of finite sized blocks of numbers. I am sampling the pattern of digits early in the string of reals, and using induction to show the structure of digits out to infinity wide, i.e. the TOTAL digit strings of all the computable reals. e.g. 006666666.. 016666666.. 106666666.. 116666666.. The structure of the first 2 digits is a complete permutation set. I prove the maximum width of complete permutations is infinity. Think of a CPS as a tall rectangle which is sampled at larger and larger sizes with induction, revealing the digit structure of the entire list (of computable reals). It's a BREADTH and DEPTH wise induction so it reveals the nature of lists more reliably than drawing a square and striking a line down the center saying NO! (that's diagonalisation if you missed the pun) > > 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. Herc
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 |