My FINAL Cantor thread!
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From: George Greene on 1 Jul 2010 17:00 On Jul 1, 4:42 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > phi(1) & An (phi(n) -> phi(n +1)) > -> > An phi(n) > > Let phi(n) = property-all-sequences holds for n. > > phi(1) & phi(2) & phi(3) = property-all-sequences holds for 1, 2 & 3. > <=> > < [1 2 3] 4 5 6...> THIS IS BULLSHIT, Herc. If it holds for 1 2 and 3 then"4 5 6..." DO NOT MATTER! You cannot justify having these rows be infinite! > > An phi(n) = property-all-sequences holds for all digits > <=> > <[1 2 3 4...]> > > That is impossible to dispute, That is just incoherent, and as I DEMONSTRATED for you, the list OF ALL FINITE PREFIXES of ANY real DOES DISPUTE and DOES REFUTE this schema! It refutes it equally well EVEN if you leave the suffixes on, as long as the suffixes do NOT MATCH the limit! For example, we could let the suffix be any string OTHER THAN PI that you like, maybe a finite one repeated infinitely (which would guarantee that the real was rational, which would guarantee that it was not equal to Pi, since Pi is irrational. Suppose the repeated suffix was .142857 (1/7). THEN, you would get THIS LIST: 3.142857142857142857 (22/7) 3.1142857142857142857 3.14142857142857142857 3.141142857142857 3.1415142857142857 3.14159142857142857 and PI WOULD NOT BE ON IT!
From: herbzet on 1 Jul 2010 17:02 George Greene wrote: > Aatu Koskensilta wrote: > > George, why do you keep yelling at |-|erc? Surely you know it won't > > accomplish anything. > > No, that is not sure at all. > I don't think people should write anyone off as "just" crazy. > There is a specific nature of disorder at work here. > I'm just investigating, basically. > For the record, I think the better question is why OTHER people > ARE NOT yelling. I know that part of THAT answer is that they > are not temperementally suited to yelling or feel that it demeans > the yeller, but I basically have no problem with that -- those of you > who think it can't be done are welcome to STAY out of the way of > those of us who are doing it. > > Nevertheless, I am willing to take this intervention as a relevant > warning. The fact that you have shown restraint heretofore greatly > enhances your credibility. I was aware that perhaps some sort of > threshold was Now being reached. Well, *I'm* ok with it. Herc perversely enjoys it too. -- hz
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 |