Why can no one in sci.math understand my simple point?
in [Logic]
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From: Peter Webb on 27 Jun 2010 08:25 "Newberry" <newberryxy(a)gmail.com> wrote in message news:8ced201d-fce9-447f-9fa9-b972f2014d8e(a)t5g2000prd.googlegroups.com... On Jun 25, 11:22 pm, "Peter Webb" <webbfam...(a)DIESPAMDIEoptusnet.com.au> wrote: > "Virgil" <Vir...(a)home.esc> wrote in message > > news:Virgil-71EA75.23485925062010(a)bignews.usenetmonster.com... > > > In article > > <b3413a4e-567b-4dfb-8037-21f14b826...(a)g1g2000prg.googlegroups.com>, > > Newberry <newberr...(a)gmail.com> wrote: > > >> > > No. (3) is not true, as it is based on a false premise (that the > >> > > computable > >> > > Reals can be listed). > > > How is countability any different from listability for an infinite set? > > > Does not countability of an infinite set S imply a surjections from N > > to S? And then does not such a surjection imply a listing? > > It implies a listing must exist, but does not provide such a listing. Does such a listing have an anti-diagonal? ________________________________ How can something which doesn't exist have some property? > The computable Reals are countable, but you cannot form them into a list > of > all computable Reals (and nothing else) where each item on the list can be > computed. > > In order to list a set, it has to be recursively enumerable. Being > countable > is not sufficient.
From: Peter Webb on 27 Jun 2010 08:26 "Virgil" <Virgil(a)home.esc> wrote in message news:Virgil-7885B6.13355726062010(a)bignews.usenetmonster.com... > In article > <8ced201d-fce9-447f-9fa9-b972f2014d8e(a)t5g2000prd.googlegroups.com>, > Newberry <newberryxy(a)gmail.com> wrote: > >> On Jun 25, 11:22 pm, "Peter Webb" >> <webbfam...(a)DIESPAMDIEoptusnet.com.au> wrote: >> > "Virgil" <Vir...(a)home.esc> wrote in message >> > >> > news:Virgil-71EA75.23485925062010(a)bignews.usenetmonster.com... >> > >> > > In article >> > > <b3413a4e-567b-4dfb-8037-21f14b826...(a)g1g2000prg.googlegroups.com>, >> > > Newberry <newberr...(a)gmail.com> wrote: >> > >> > >> > > No. (3) is not true, as it is based on a false premise (that the >> > >> > > computable >> > >> > > Reals can be listed). >> > >> > > How is countability any different from listability for an infinite >> > > set? >> > >> > > Does not countability of an infinite set S imply a surjections from N >> > > to S? And then does not such a surjection imply a listing? >> > >> > It implies a listing must exist, but does not provide such a listing. >> >> Does such a listing have an anti-diagonal? > > Every list of reals, or of infinite binary sequences, has an > antidiagonal, in fact, has at least as many antidiagonals as elements. >> >> > The computable Reals are countable, but you cannot form them into a >> > list of >> > all computable Reals (and nothing else) where each item on the list can >> > be >> > computed. >> > >> > In order to list a set, it has to be recursively enumerable. Being >> > countable >> > is not sufficient. > > In order explicitely to construct such a list, perhaps, but such lists > may exist even when not explicitely constructable. And for any countable > set, they do. Well, Cantor used the list explicitly in his construction.
From: Jesse F. Hughes on 27 Jun 2010 08:58 Tim Little <tim(a)little-possums.net> writes: > On 2010-06-27, Jesse F. Hughes <jesse(a)phiwumbda.org> wrote: >> The usual definitions of computable real require that the machine >> accept input n, halts and outputs the first n digits, or something >> like that. > > There are a number of definitions, all of which end up being provably > equivalent. The definition CB has so far provided is a particularly > bizarre one, but does still appear to be equivalent. I haven't seen his definition, but he seems to suggest that the machine that repeatedly overwrites a single square with 0 or 1 computes a real number. Is that consistent with his definition? -- "Being who I am, I know that's a solution that will run in polynomial time, but for the rest of you, it will take a while to figure that out and know why [...But] it's the same principle that makes n! such a rapidly growing number." James S. Harris solves Traveling Salesman
From: Frederick Williams on 27 Jun 2010 11:05 |-|ercules wrote: > > The answer to your question 'Why can no one in sci.math understand my simple point?' is that none of them are your intellectual equal. -- I can't go on, I'll go on.
From: Newberry on 27 Jun 2010 12:14
On Jun 26, 12:35 pm, Virgil <Vir...(a)home.esc> wrote: > In article > <8ced201d-fce9-447f-9fa9-b972f2014...(a)t5g2000prd.googlegroups.com>, > > > > > > Newberry <newberr...(a)gmail.com> wrote: > > On Jun 25, 11:22 pm, "Peter Webb" > > <webbfam...(a)DIESPAMDIEoptusnet.com.au> wrote: > > > "Virgil" <Vir...(a)home.esc> wrote in message > > > >news:Virgil-71EA75.23485925062010(a)bignews.usenetmonster.com... > > > > > In article > > > > <b3413a4e-567b-4dfb-8037-21f14b826...(a)g1g2000prg.googlegroups.com>, > > > > Newberry <newberr...(a)gmail.com> wrote: > > > > >> > > No. (3) is not true, as it is based on a false premise (that the > > > >> > > computable > > > >> > > Reals can be listed). > > > > > How is countability any different from listability for an infinite set? > > > > > Does not countability of an infinite set S imply a surjections from N > > > > to S? And then does not such a surjection imply a listing? > > > > It implies a listing must exist, but does not provide such a listing. > > > Does such a listing have an anti-diagonal? > > Every list of reals, or of infinite binary sequences, has an > antidiagonal, in fact, has at least as many antidiagonals as elements. I was replying to this: "It implies a listing must exist, but does not provide such a listing." "It", in this context is the statement "all computable reals are countable." If an antidiagonal existed it would prove that there was no such list. > > > > > > The computable Reals are countable, but you cannot form them into a list of > > > all computable Reals (and nothing else) where each item on the list can be > > > computed. > > > > In order to list a set, it has to be recursively enumerable. Being countable > > > is not sufficient. > > In order explicitely to construct such a list, perhaps, but such lists > may exist even when not explicitely constructable. And for any countable > set, they do.- Hide quoted text - > > - Show quoted text - |