Le 20-nov.-07, à 23:39, Barry Brent wrote :
> > You're saying that, just because you can *write down* the missing > sequence (at the beginning, middle or anywhere else in the list), it > follows that there *is* no missing sequence. Looks pretty wrong to me. > > Cantor's proof disqualifies any candidate enumeration. You respond > by saying, "well, here's another candidate!" But Cantor's procedure > disqualified *any*, repeat *any* candidate enumeration. > > Barry Brent Torgny, I do agree with Barry. Any bijection leads to a contradiction, even in some effective way, and that is enough (for a classical logician). But look what you write: > On Nov 20, 2007, at 11:42 AM, Torgny Tholerus wrote: > >> >> An ultrafinitist comment to this: >> ====== >> You can add this complementary sequence to the end of the list. >> That will make you have a list with this complementary sequence >> included. >> >> But then you can make a new complementary sequence, that is not >> inluded. But you can then add this new sequence to the end of the >> extended list, and then you have a bijection with this new sequence >> also. And if you try to make another new sequence, I will add that >> sequence too, and this I will do an infinite number of times. How could an ultrafinitist refute an argument by saying "... and this I will do an infinite number of times. "? >> So >> you will not be able to prove that there is no bijection... Actually no. If you do what you described omega times, you will just end up with a set which can still be put in 1-1 correspondence with N (as shown in preceding posts on bijections) To refute Cantor, here, you should do what you described a very big infinity of times, indeed an non enumerable infinity of times. But then you have to assume the existence of a non enumerable set at the start. OK? Bruno http://iridia.ulb.ac.be/~marchal/ >> ====== >> What is wrong with this conclusion? >> >> -- >> Torgny >> >>> > > Dr. Barry Brent > [EMAIL PROTECTED] > http://home.earthlink.net/~barryb0/ > > > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
