A BLATENT FLAW in Cantor's diag proof
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From: |-|ercules on 8 Jun 2010 23:16 "George Greene" <greeneg(a)email.unc.edu> wrote > On Jun 8, 4:29 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> YOU CAN'T FIND A NEW DIGIT SEQUENCE AT ANY POSITION ON THE COMPUTABLE REALS. > > OF COURSE you can't find it "at any position". > It is INFINITELY long and the differences occur at INFINITELY MANY > DIFFERENT positions! > >>. - N O . N E W . D I G I T . S E Q U E N C E > > The anti-diagonal IS ALWAYS a new digit sequence, > DUMBASS. You seem to be backpedaling like the others now, that a computable list is impossible anyway so I can't use it in my argument. Just answer my other reply to your other moronic post, this is the question now. How many natural numbers are there in "all natural numbers"? Have a shot! (in the other thread in context) Herc
From: George Greene on 8 Jun 2010 23:29 On Jun 8, 4:33 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > Is a *new digit sequence* missing from the list? Of course. The anti-diagonal OF ANY square list IS MISSING from the list. > >> All possible digit sequences are computable to all, as in an infinite amount of, finite lengths This is just bullshit. If you knew how to define "computable" then you would know that computer programs and computer memories HAVE TO BE FINITE. This means that there are at most countably infinitely many of them. Conveniently, THIS IS THE SAME infinity as the infinite number of digit positions in a real. It is the SMALLEST infinity. It is the infinity where EVERY part/ position withIN the infinity IS FINITE AS OPPOSED to infinite. The fact that the number of computers and the number of digit- positions are THE SAME infinity means that the list of computable reals is square. So it has a diagonal that is the SAME length as a real (that IS a real). It therefore has an anti-diagonal that is a real, and IS NOT ON the list. THAT MAKES IT "new" if your "old" reals were the ones ON the list.
From: George Greene on 8 Jun 2010 23:36 On Jun 8, 8:10 pm, Tim Little <t...(a)little-possums.net> wrote: > You need to be careful here. A computable list must contain only > computable numbers, but not all lists of computable numbers are > computable lists. This is a stupid point. If you order the list properly then the list will be computable as well. You would have to get intentionally perverse to get the list into an un-computable order, and since it's YOU doing it (and you're a finite human), even You might NOT be able to MANAGE to get it into a computable order. You DON'T NEED "all lists". JUST ONE [denumerably long] computable list of all the [denumerably wide] computable numbers is enough for Herc (regardless of whether you're attacking or defending him).
From: George Greene on 8 Jun 2010 23:39 On Jun 8, 8:22 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > Here's what's funny about USENET. In a regular classroom, > you have one teacher and many students. In a typical USENET > discussion, there are many teachers and just one student. > You'd think that such a low student/teacher ratio would make > for quick progress, but that doesn't turn out to be the case. This is true, but it's not for the reason you think. The reason for the lack of progress is THE STUPID HALF of the alleged teachers. The stupider the student is, the greater will be the number of semi-stupid people who are smarter-enough-than-him that they will mistake themselves for able-to-teach-him. The stupid student can therefore IGNORE what is said by the smart teachers while engaging with the semi-stupid ones, most of whom he will PROPERLY refute -- which will just INcrease his confidence in his own errors. And the narcissism deepens. Unfortunately, the narcissist does not waste away.
From: George Greene on 8 Jun 2010 23:42
> "William Hughes" <wpihug...(a)hotmail.com> wrote > > Is this digit sequence (which does not have a last 3) > > > 33333... > > > in this list > > > 1 3 > > 2 33 > > 3 333 > > ... > > > of sequences (all of which have a last 3). > > > Yes or No. I said it first. Herc replied (astoundingly) > No. If you actually believe this, then why do you keep talking about how having "every digit sequence" MATTERS? THIS LIST HAS EVERY digit sequence, up to EVERY finite length, MATCHING .33333.... ! NAME ME ONE POSITION where this list of FINITE strings DOESN'T MATCH ..3333.....! YOU CAN'T!! Yet DESPITE this, .3333.... IS NOT ON THIS LIST! YOU YOURSELF JUST SAID SO! So why are you having so much trouble noticing that EVEN if you have EVERY possible FINITE initial sequence somewhere on your list of computable reals, you still DON'T have many infinite ones (and you provably do NOT have the infinite anti-diagonal, since that PROVABLY DIFFERS from EVERYthing you DO have on the list!)? |