My FINAL Cantor thread!
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From: George Greene on 1 Jul 2010 16:45 On Jul 1, 7:06 am, Don Stockbauer <donstockba...(a)hotmail.com> wrote: > Just 2 infinities: > > 1. Potential. > > 2. Actualized. Oh, GOD, no. Not THAT again. There is no such thing as potential infinity, but if that's what it takes to get Herc to see the difference, maybe I would tolerate it. An infinite number of finite things IS NOT "potential infinity". It is AN ACTUAL infinity OF finite things! The point is that there is no INFINITE thing in the collection, DESPITE the fact that infinity is THE SIZE of the collection. Obviously, there is a difference between a number being THE SIZE of a collection and A MEMBER of the collection. {0,1,2,3,4,5} has a SIZE of 6 but 6 IS NOT a MEMBER of it! THAT and NOT "potential v. actualized" is the RELEVANT distinction. One of "the real underlying problems" with people with Herc's and WM's disease is that they think that the natural numbers start with 1. AROUND HERE, WE COUNT FROM ZERO. At the BEGINNING of the journey, you have taken ZERO steps, NOT ONE, YET. At the beginning of the marriage, you have (barring accidents) ZERO children, NOT ONE, YET. In the finite case, if you start counting with 1 and you have 7 things, then the last one must BE 7; the size MUST be an ELEMENT of the set. Herc et al think this "must" carry over to "the infinite" case, "by induction". This IS JUST BULLSHIT, but the POINT is, what ACTUALLY happens, WILL carry over to the finite case analogously, IF you count FROM ZERO instead of from 1; THEN, the size will be the-smallest-thing-that-is-BIGGER-than everything in the set. And the POINT will be that, BEING BIGGER than everything in the set, IT IS *NOT*IN* the set!
From: George Greene on 1 Jul 2010 16:46 > 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".
From: George Greene on 1 Jul 2010 16:54 On Jul 1, 4:42 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "George Greene" <gree...(a)email.unc.edu> wrote > phi(1) & An (phi(n) -> phi(n +1)) > -> > An phi(n) > > Let phi(n) = property-all-sequences holds for n. YOU CANNOT let phi(n) be "property all-sequences holds for n". Property all-sequences DOES NOT hold for n! Property all-sequences ONLY holds FOR the WHOLE INFINITE list!! Maybe you should try STATING THE RELEVANT PROPERTY OF n FORMALLY so YOU WILL HAVE A CLUE. One way you COULD make property-all-sequences hold for n IS BY HAVING A LIST *OF FINITE* sequences instead of reals. You could have the first element have 10 digits -- all the *1*-digit prefixes, ..0123456789, the second element have 200 digits (all the 2-digit prefixes), ..0001020304050607080910111213141516171819202122232425etc.. the third element have 3000 digits, the 4th element have 40000 digits, the 5th element have 500000 digits, and the 6th element have 6 million digits, etc. THEN it would be the case that the nth element of the list contained in it, somewhere, all possible length-n-prefixes-of-EVERY-real. THEN phi(n) would be "property all-sequences holds for n". Of course, since all these lists ARE FINITE, you COULD just CONCATENATE ALL of them INTO ONE computable real. Even having a LIST at ALL is JUST STUPID if ALL you are trying to achieve is "property all-sequences". Just what property-all- sequences IS A PROPERTY *OF* is something that you do NOT understand.
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 |