Adriana Xenides Dead
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From: William Hughes on 7 Jun 2010 20:08 On Jun 7, 7:53 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "William Hughes" <wpihug...(a)hotmail.com> wrote .. > > > > > On Jun 7, 6:46 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > >> "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote > > >> > "|-|ercules" <radgray...(a)yahoo.com> writes: > > >> >>>> Given a set of labeled boxes containing numbers inside them, > >> >>>> can you possibly find a box containing all the label numbers of boxes > >> >>>> that don't contain their own label number? > > >> >> Have a go mate! > > >> > The answer is no, near as I can figure. > > >> > Now, if you also knew that, for each set of numbers, there is a box > >> > containing that set, then you'd have a paradox. Near as I can figure, > >> > you *don't* know that. > > >> > In set theory, on the other hand, we *do* know the analogous claim. > > >> So, no box ever containing the numbers of boxes not containing their own numbers > >> means higher infinities exist? > > > Yes. > > > - William Hughes > > Good. After 4 days you've been given the OK by Ullrich's sidekick to admit, err... > > No box ever containing the numbers of boxes not containing their own number > means higher infinities exist. > err... Yes - William Hughes
From: Jesse F. Hughes on 7 Jun 2010 20:10 "|-|ercules" <radgray123(a)yahoo.com> writes: > "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote >> "|-|ercules" <radgray123(a)yahoo.com> writes: >> >>>>> Given a set of labeled boxes containing numbers inside them, >>>>> can you possibly find a box containing all the label numbers of boxes >>>>> that don't contain their own label number? >>> >>> Have a go mate! >> >> The answer is no, near as I can figure. >> >> Now, if you also knew that, for each set of numbers, there is a box >> containing that set, then you'd have a paradox. Near as I can figure, >> you *don't* know that. >> >> In set theory, on the other hand, we *do* know the analogous claim. > > So, no box ever containing the numbers of boxes not containing their own numbers > means higher infinities exist? *Given* that every set of numbers is contained in some box, I guess so. But I don't see how this analogy is supposed to make Cantor's theorem appear dubious. -- Jesse F. Hughes "Well, I'm a pragmatist. I've been wrong MANY TIMES and it seems to me that it would be simpler to be wrong with this paper." --James S. Harris explains his latest paper
From: |-|ercules on 7 Jun 2010 21:35 "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote > "|-|ercules" <radgray123(a)yahoo.com> writes: > >> "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote >>> "|-|ercules" <radgray123(a)yahoo.com> writes: >>> >>>>>> Given a set of labeled boxes containing numbers inside them, >>>>>> can you possibly find a box containing all the label numbers of boxes >>>>>> that don't contain their own label number? >>>> >>>> Have a go mate! >>> >>> The answer is no, near as I can figure. >>> >>> Now, if you also knew that, for each set of numbers, there is a box >>> containing that set, then you'd have a paradox. Near as I can figure, >>> you *don't* know that. >>> >>> In set theory, on the other hand, we *do* know the analogous claim. >> >> So, no box ever containing the numbers of boxes not containing their own numbers >> means higher infinities exist? > > *Given* that every set of numbers is contained in some box, I guess > so. > > But I don't see how this analogy is supposed to make Cantor's theorem > appear dubious. So, as many have put it, the holy grail of mathematics, the infinite paradise is based on no box containing the numbers of boxes that don't contain their own number? Herc
From: |-|ercules on 8 Jun 2010 02:30 > "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote >> But I don't see how this analogy is supposed to make Cantor's theorem >> appear dubious. What about this statement? All possible digit sequences are computable to all, as in an infinite amount of, finite lengths. Herc
From: Tim Little on 8 Jun 2010 03:24
On 2010-06-08, |-|ercules <radgray123(a)yahoo.com> wrote: > What about this statement? > > All possible digit sequences are computable to all, as in an > infinite amount of, finite lengths. What about it? Apart from being an example of a mathematically ambiguous statement with at least 3 reasonable interpretations, 2 of which make it false and 1 makes it true, that is. - Tim |