My FINAL Cantor thread!
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From: |-|ercules on 5 Jul 2010 08:36 "George Greene" <greeneg(a)email.unc.edu> wrote >> <[1 2] 3 4 ...> >> >> is not the real 0.12 or 0.1234... >> nor the sequence <1 2> or <1 2 3 4..> > > IT IS SO TOO the sequence <1 2>, for the purpose for which you are > trying to use it. > The stuff after the [1 2] DOES NOT MATTER in your treatment. We'll skip the ambiguity over the 3 meanings of digit there. It's the 'covered sequences' within the infinite sequences that approaches infinity. For each subset of reals, there exists a maximum digit length that that subset doesn't miss a possible sequence of initial digits of that digit length. Binary example 00000000... 01111111... 01011111... 01000000... 01010101... 00111111... 11111111... 11000000... 11011111... 10000000... 10111111... 11000000... The length of all (initial) possible digit sequences within the set is 3. Want to see a bigger list and see what happens? Herc
From: George Greene on 5 Jul 2010 14:39 On Jul 5, 8:36 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > It's the 'covered sequences' within the infinite sequences > that approaches infinity. Then you have to DEFINE COVERED, dumbass! And IF all you want to do is COVER the sequences, THE THE LIST OF FINITE prefixes WILL DO that! YOU DON'T NEED even ONE infinitely long real, JUST TO COVER the sequences! The list of all finite sequences OBVIOUSLY COVERS all FINITE prefixes, since a finite sequence and a finite prefix ARE THE SAME THING!!
From: |-|ercules on 5 Jul 2010 19:29 "George Greene" <greeneg(a)email.unc.edu> wrote > On Jul 5, 8:36 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> It's the 'covered sequences' within the infinite sequences >> that approaches infinity. > > Then you have to DEFINE COVERED, dumbass! > And IF all you want to do is COVER the sequences, > THE THE LIST OF FINITE prefixes WILL DO that! > YOU DON'T NEED even ONE infinitely long real, JUST TO COVER the > sequences! > The list of all finite sequences OBVIOUSLY COVERS all FINITE prefixes, > since > a finite sequence and a finite prefix ARE THE SAME THING!! No they're not, a finite sequence has a terminating suffix. There is a distinction between sampling the one object and considering multiple different objects. You saying YES THEY ARE a hundred times is like a musician arguing his lyrics were copied. But I've done enough on this topic this round, if I come up with some formal distinction then in the words of Arnold Schwarzenegger I'LL BE BACK! Herc
From: George Greene on 5 Jul 2010 21:02 On Jul 5, 7:29 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > But I've done enough on this topic this round, No, you haven't. You still haven't DEFINED what it means for a LIST to COVER a SEQUENCE (finite or otherwise -- if the list is infinite then it can also cover an infinite sequence). > if I come up with some formal distinction You DON'T NEED a distinction -- formal or otherwise -- between "finite prefix" and "finite sequence" BECAUSE THERE ISN'T ANY -- EVERY finite prefix IS a finite sequence and EVERY finite sequence IS a finite prefix. What you DO need is a formal DEFINITION of COVERED. If you would ever write one then you would see that you are getting the quantifiers switched around.
From: |-|ercules on 5 Jul 2010 22:07
"George Greene" <greeneg(a)email.unc.edu> wrote > On Jul 5, 7:29 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> "George Greene" <gree...(a)email.unc.edu> wrote >> >> > On Jul 5, 8:36 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> >> It's the 'covered sequences' within the infinite sequences >> >> that approaches infinity. > > You still have to DEFINE COVERED, DUMBASS. You made a post last week using some word to mean what I mean, but I shan't bother looking for it. > And it DOES NOT "approach infinity". It just STAYS FINITE ALL the > time. Binary example 00000000... 01111111... 01011111... 01000000... 01010101... 00111111... 11111111... 11000000... 11011111... 10000000... 10111111... 11000000... The length of all (initial) possible digit sequences within the set is 3. So you are saying this length does not approach infinity as the length of the computable reals list approaches infinity? Herc |