halting problem proof, via diagonalization?
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From: Balthasar on 8 Aug 2008 14:21 On Fri, 8 Aug 2008 11:10:36 -0700 (PDT), MoeBlee <jazzmobe(a)hotmail.com> wrote: > > Whether the list is infinite or NOT, the anti-diagonal is not on the > list. > Wait a second, Moe! This is not necessarily the case. Actually: "For every line of Cantor's list it is true that this line does not contain the diagonal number. Nevertheless the diagonal number may be in the infinite list." (WM) Try to get that straight! B.
From: Balthasar on 8 Aug 2008 14:22 On Fri, 08 Aug 2008 20:08:16 +0200, Balthasar <nomail(a)invalid> wrote: > suppose "propose", of course. B.
From: tchow on 8 Aug 2008 14:36 In article <8qvo941tgkic4arebdsd32gbt1f63pl2h8(a)4ax.com>, Balthasar <nomail(a)invalid> wrote: >Not though that there's still a loophole mentioned by WM! (See signature >below.) >-- >"For every line of Cantor's list it is true that this line does not > contain the diagonal number. Nevertheless the diagonal number may > be in the infinite list." (WM, sci.logic) This is an amusing one. So a number may be "in" a list of numbers without being in any *line* of the list? The whole is greater than the sum of its parts, or something like that? A list can contain things that don't appear in any line of the list? But then where exactly are these things located? And how can you tell whether some non-line-item is *in* the list rather than *after* the list, or above the list, or through the list, or between the list, or just hanging around the neighborhood for the joy of rubbernecking? -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
From: Alan Smaill on 8 Aug 2008 14:41 tchow(a)lsa.umich.edu writes: > In article <8qvo941tgkic4arebdsd32gbt1f63pl2h8(a)4ax.com>, > Balthasar <nomail(a)invalid> wrote: > >Not though that there's still a loophole mentioned by WM! (See signature > >below.) > >-- > >"For every line of Cantor's list it is true that this line does not > > contain the diagonal number. Nevertheless the diagonal number may > > be in the infinite list." (WM, sci.logic) > > This is an amusing one. So a number may be "in" a list of numbers without > being in any *line* of the list? The whole is greater than the sum of its > parts, or something like that? A list can contain things that don't appear > in any line of the list? But then where exactly are these things located? > And how can you tell whether some non-line-item is *in* the list rather than > *after* the list, or above the list, or through the list, or between the > list, or just hanging around the neighborhood for the joy of rubbernecking? I'm told that intelligent people "read between the lines" ... > -- > Tim Chow tchow-at-alum-dot-mit-dot-edu > The range of our projectiles---even ... the artillery---however great, will > never exceed four of those miles of which as many thousand separate us from > the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences -- Alan Smaill
From: Balthasar on 8 Aug 2008 14:43
On 08 Aug 2008 18:36:52 GMT, tchow(a)lsa.umich.edu wrote: >> >> Note though that there's still a loophole mentioned by WM! >> >> "For every line of Cantor's list it is true that this line does not >> contain the diagonal number. Nevertheless the diagonal number may >> be in the infinite list." (WM, sci.logic) >> > This is an amusing one. So a number may be "in" a list of numbers without > being in any *line* of the list? The whole is greater than the sum of its > parts, or something like that? A list can contain things that don't appear > in any line of the list? But then where exactly are these things located? > And how can you tell whether some non-line-item is *in* the list rather than > *after* the list, or above the list, or through the list, or between the > list, or just hanging around the neighborhood for the joy of rubbernecking? > *lol* Well, WM is certainly an artist, no question. :-) B. |