My FINAL Cantor thread!
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From: |-|ercules on 1 Jul 2010 19:42 "George Greene" <greeneg(a)email.unc.edu> wrote >> On Jul 1, 4:06 am, Don Stockbauer <donstockba...(a)hotmail.com> wrote: >> >> >> >> > Just 2 infinities: >> >> > 1. Potential. >> >> > 2. Actualized. > > On Jul 1, 11:51 am, Marshall <marshall.spi...(a)gmail.com> wrote: >> Wow, the cranks are really coming out in force now. Maybe Herc >> is the crank messiah! > > Thank you, Marshall. You may now have 1 "AMEN". Talk about thick as 2 planks. This induction method holds for any [property]. phi( <[1] 2 3 4...> ) & An (phi ( <[1 2 ... n] n+1 n+2 ...>) -> phi( <[1 2 ... n n+1] n+2 n+3 ...> )) -> phi( <[1 2 3 4...]> ) Herc
From: George Greene on 2 Jul 2010 01:42 On Jul 1, 7:42 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > This induction method holds for any [property]. This IS NOT an "induction method", > phi( <[1] 2 3 4...> ) & An (phi ( <[1 2 ... n] n+1 n+2 ...>) -> phi( <[1 2 ... n n+1] n+2 n+3 ...> )) > -> > phi( <[1 2 3 4...]> ) and it DOES NOT HOLD for the property of "the n digits in the [..]'s all MATCH Pi (or whatever real you are talking about!) and ARE ON THE LIST"! <[1 2 3 4...]> would, in this case, BE Pi, and phi(Pi) would be "Pi IS ON THE LIST", but Pi IS NOT ON the list of all finite prefixes of Pi, NOR is it on a list of those finite prefixes each-infinitely-extended by some infinite suffix that is NOT a suffix of Pi! What ACTUALLY goes after the --> is An[Phi(n)], but what YOU have after the arrow DOES NOT HAVE AN n IN it!!
From: |-|ercules on 2 Jul 2010 02:52 "George Greene" <greeneg(a)email.unc.edu> wrote > On Jul 1, 7:42 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> This induction method holds for any [property]. > > This IS NOT an "induction method", >> phi( <[1] 2 3 4...> ) & An (phi ( <[1 2 ... n] n+1 n+2 ...>) -> phi( <[1 2 ... n n+1] n+2 n+3 ...> )) >> -> >> phi( <[1 2 3 4...]> ) > > and it DOES NOT HOLD for the property of "the n digits in the [..]'s > all MATCH Pi > (or whatever real you are talking about!) and ARE ON THE LIST"! > <[1 2 3 4...]> would, in this case, BE Pi, and phi(Pi) would be "Pi IS > ON THE LIST", > but Pi IS NOT ON the list of all finite prefixes of Pi, NOR is it on a > list of those finite > prefixes each-infinitely-extended by some infinite suffix that is NOT > a suffix of Pi! > > What ACTUALLY goes after the --> is An[Phi(n)], but what YOU have > after the arrow DOES NOT HAVE AN n IN it!! An [n] [x] [y] <-> [x y] You're a dope. Every time I use induction on a PROPERTY of digits, you go on about SEQUENCE OF DIGITS (i.e. reals). I'm not using induction on a sequence of digits, not directly, I'm using induction on a property of digit positions of the list of computable reals. <[1 2] 3 4 ...> is not the real 0.12 or 0.1234... nor the sequence <1 2> or <1 2 3 4..> is is the 2 digit wide matrix of the 2 leftmost columns of the list of computable reals. [ 04 24 30 05 03 22 00 99 31 .... ] phi( <[1 2] 3 4 ...> ) is the property that that matrix contains all possible sequences of length 2. Next you'll be telling me I can't mow an infinite lawn... http://i721.photobucket.com/albums/ww214/ozdude7/fencingVSmowing.png Here's the story again that tells of the difference to Sylvia's finite sequence induction. You and I start a landscaping business Herc And Syl's Landscaping Ad Infinitum I handle all the mowing, and you do the fencing. We get a call from Mr Fenceme and Mrs Mowme Blockheads. We drive to the property which appears to be divided into 2 blocks, both infinite rectangular lawns. On one block, you start doing the fencing for Mr Fenceme, completing the perimeters of larger and larger concentric rectangular paddocks. I get to the mowing for Mrs Mowme, completing larger and larger rectangular mown lawn areas, each building upon the earlier smaller rectangular lawn area. I'm well on my way to mowing the whole lawn. You never ever come close to fencing the entire lawn! ;-) The limit of mown lawn area as mowing time->oo is infinity. However, infinitely many fence sizes all have finite perimeters. George won't be able to tell the difference. Herc
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!! |