A BLATENT FLAW in Cantor's diag proof
in [Math]
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From: David Bernier on 9 Jun 2010 04:06 Sylvia Else wrote: > On 9/06/2010 1:50 PM, Aatu Koskensilta wrote: >> stevendaryl3016(a)yahoo.com (Daryl McCullough) writes: >> >>> I don't think that's correct. There is no teacher that is >>> capable of explaining anything to Herc. >> >> Yet there is no shortage of people strangely willing to give it a try. >> > > Er, that's an assumption. People who appear to be attempting to explain > something to Herc may in fact be doing something else entirely, such as > trying to understand how Herc's mind works. > > Herc appears to have a diverse set of false beliefs that he expresses on > Usenet. What I've been hoping to get is a handle on is whether all of > these false beliefs are delusions arising from his mental illness, or > whether some of them are just conventional beliefs of falsehoods, of the > kind found often enough even in people considered sane. > > Of course, there may not be a clear line dividing categories of false > beliefs. > > What's disconcerting is how fragile is the brain's grip on reality, such > that some obscure chemical imbalance can destroy it. This reminds me of trying to distinguish facts from opinions. I think it's useful to attach varying degrees of belief to "facts". For example, when does something that's reported in "Breaking News" become a fact? Pluto used to be a planet, but now it isn't a planet anymore. I think every once in a while, most sane people will make a fall inference; afterwards, they might say: "Oh, I never thought about that." David Bernier
From: Sylvia Else on 9 Jun 2010 04:27 On 9/06/2010 6:06 PM, David Bernier wrote: > For example, when does something that's reported in "Breaking News" > become a fact? For many news outlets, never. > Pluto used to be a planet, but now it isn't a planet anymore. Only if you believe that the International Astronomical Union has the power to determine the meanings of English words. Sylvia.
From: |-|ercules on 9 Jun 2010 05:17 "Sylvia Else" <sylvia(a)not.here.invalid> wrote > On 9/06/2010 6:06 PM, David Bernier wrote: > >> For example, when does something that's reported in "Breaking News" >> become a fact? > > For many news outlets, never. > >> Pluto used to be a planet, but now it isn't a planet anymore. > > Only if you believe that the International Astronomical Union has the > power to determine the meanings of English words. > > Sylvia. You seem firm in your beliefs, and the meaning of the post is lost on you yet again. Herc
From: William Hughes on 9 Jun 2010 08:01 On Jun 9, 3:57 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "William Hughes" <wpihug...(a)hotmail.com> wrote > > > > > On Jun 9, 12:13 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > >> "William Hughes" <wpihug...(a)hotmail.com> wrote > > >> > On Jun 8, 11:21 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > >> >> "William Hughes" <wpihug...(a)hotmail.com> wrote > > >> >> > On Jun 8, 6:17 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > >> >> >> "William Hughes" <wpihug...(a)hotmail.com> wrote > > >> >> >> > On Jun 8, 5:52 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > >> >> >> >> "William Hughes" <wpihug...(a)hotmail.com> wrote > > >> >> >> >> > On Jun 8, 5:39 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > >> >> >> >> >> "William Hughes" <wpihug...(a)hotmail.com> wrote > > >> >> >> >> >> > On Jun 8, 5:29 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > > >> >> >> >> >> >> The infinitely many long sequences of all possible digit sequences DOESN'T MISS A SEQUENCE OF DIGITS. > > >> >> >> >> >> > Since every sequence has a last digit, any sequence > >> >> >> >> >> > of digits that does not have a last digit is missed. > > >> >> >> >> >> You're as confused as when you said there is no algorithm to produce an infinite list. > > >> >> >> >> >> Herc > > >> >> >> >> > 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. > > >> >> >> >> > - William Hughes > > >> >> >> >> No. > > >> >> >> > So a list of sequences with last digit will miss > >> >> >> > a sequence without last digit. > > >> >> >> > - William Hughes > > >> >> >> Yes, this is a fine QUANTITATIVE argument that SUPPORTS *missing sequences*, using an example of a converging sequence. > > >> >> >> Unfortunately a rudimentary QUALITATIVE analysis contradicts that modifying the diagonal results in a new sequence of > >> >> >> digits. > > >> >> > Nope, The list contains only sequences with last digit. A sequence > >> >> > without last digit is a sequence that > >> >> > is not contained in the list. > > >> >> > - William Hughes > > >> >> Is pi computable? > > >> > Yes. However, it is not in the list. The list contains > > >> > 3 > >> > 31 > >> > 314 > >> > 3145 > >> > ... > > >> > It does not contain pi. > > >> > - William Hughes > > >> Your argument seems to be there is uncountable infinity because computers can only calculate a finite number of digits. > > > No, I have never mentioned computers and the fact that computers > > can only calculate a finite number of digits > > is entirely irrelevant. > > - William Hughes > > Wasn't it you who said the computer would never get to the second real if the first was > 00000... > > Herc No.
From: William Hughes on 9 Jun 2010 08:06
On Jun 9, 12:36 am, George Greene <gree...(a)email.unc.edu> wrote: > 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. Nope. E.g. there is no way to order the list of all computable numbers to make it a computable list. - William Hughes |