Can N be constructed?
in [Logic]
|
Prev: "NO BOX CONTAINS THE BOX NUMBERS THAT DON'T CONTAIN THEIR OWN BOX NUMBER" ~ XEN
Next: "NO BOX CONTAINS THE BOX NUMBERS THAT DON'T CONTAIN THEIR OWN BOX NUMBER" ~ XEN
From: WM on 12 Jun 2010 09:19 On 11 Jun., 22:57, Virgil <Vir...(a)home.esc> wrote: > > > Actually that is NOT what Cantor says in his "diagonal" argument. What > > > Cantor does say is that for every list of infinite binary sequences > > > presented he can construct a binary sequence not in that list. > > > What would be the result of the construction as long as it is > > unfinished? > > That is not Cantor's problem to solve. > It is. Cantor stated that the process of comparing digits must be finished instantaneously. That statement is wrong. > > > > Look here for instance, if you want to have the opinion of an expert: > >http://groups.google.de/group/sci.math.research/browse_frm/thread/4a8... > > 04ad# > > There are 'experts' on both sides of the issue, with physicists on one > side and mathematicians on the other. > > But, for example, the mathematics of coding, on which a huge amount of > modern commerce is deeply dependant, is entirely and exclusively > non-physics. > > So there are important, even essential, areas of mathematics in which > physics has absolutely no part. Who does that coding? Brains, pencils, computers? What would happen without matter, without energy, without physics? Regards, WM
From: David R Tribble on 12 Jun 2010 12:51 WM wrote: >> It is not necessary to stop somewhere in order to remain in the finite >> domain. > David R Tribble wrote: >> If you don't stop at any finite step, how can the list be incomplete? > WM wrote: > That is the characteristic feature of an infinite list. Non sequitur. The list is incomplete (only) at every finite step. But if you don't stop at any finite step, how can the list be incomplete? You say the list is incomplete, therefore there must be some step at which you are stopping to make it so. Which step?
From: David R Tribble on 12 Jun 2010 12:55 WM wrote: >> My proof does not show which line is left. But it shows that finished >> infinity is a non-mathematical notion. Of course it is always the last >> line that is left, and it is impossible to get rid of a last line, >> though the contents of the last line may change as often as desired. > David R Tribble wrote: >> Non sequitur. If the contents of the last line changes, then >> obviously that must be a different last line. There must therefore >> be more than one line you call the "last line". > WM wrote: >> The last line only temporarily deserves that name. > David R Tribble wrote: >> Then there is no last line at all. > WM wrote: > So it is. At least there is no last line - after all. Correct. There is an infinite list of lines, where each line is written at each step, but no last line.
From: David R Tribble on 12 Jun 2010 13:06 Virgil wrote: >> [Mathematical encryption encoding] >> So there are important, even essential, areas of mathematics in which >> physics has absolutely no part. > WM wrote: > Who does that coding? Brains, pencils, computers? What would happen > without matter, without energy, without physics? I believe this kind of logical error is a "domain error", or simply a "reification fallacy": http://en.wikipedia.org/wiki/Reification_(fallacy) Abstract ideas are encoded in our physical brains, yes. But how does that turn mathematical and logic equations into physics equations?
From: WM on 12 Jun 2010 13:20
On 12 Jun., 18:51, David R Tribble <da...(a)tribble.com> wrote: > WM wrote: > >> It is not necessary to stop somewhere in order to remain in the finite > >> domain. > > David R Tribble wrote: > >> If you don't stop at any finite step, how can the list be incomplete? > > WM wrote: > > That is the characteristic feature of an infinite list. > > Non sequitur. The list is incomplete (only) at every finite step. And there is no other. > But if you don't stop at any finite step, how can the list be > incomplete? That is the property of infinity. > > You say the list is incomplete, therefore there must be some > step at which you are stopping to make it so. Non sequitur. > Which step?cannot become complete. None. The list is incomplete after every step. Regards, WM |