Re: Cantor's Diagonal
Hi, Because zero even repeated an infinity of time is zero and is a natural number. (1,1,1,...) can't be a natural number because it is not finite and a natural number is finite. If it was a natural number, then N would not have a total ordering. Ok agreed: I was caught up in viewing it simply as an indexing scheme, but viewed constructively I of course agree. My error. I am becoming more and more an ultra-finitist. Arguments with infinity seem to be very based on the assumptions you make (about platonia or whatever) Finite and infinite concepts are dual concepts you can't leave one without leaving the other. Could you elaborate some more on this? Regards, Günther -- Günther Greindl Department of Philosophy of Science University of Vienna [EMAIL PROTECTED] http://www.univie.ac.at/Wissenschaftstheorie/ Blog: http://dao.complexitystudies.org/ Site: http://www.complexitystudies.org --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: Cantor's Diagonal
Hi, Le Friday 21 December 2007 13:08:38 Günther Greindl, vous avez écrit : Hi Russell, Russell Standish wrote: In your first case, the number (1,1,1,1...) is not a natural number, since it is infinite. In the second case, (0,0,0,...) is a natural number, but is also on the list (at infinity). Why is (1,1,1,...) not in the list but (0,0,0,...) in the list at infinity? This seems very arbitrary to me. Because zero even repeated an infinity of time is zero and is a natural number. (1,1,1,...) can't be a natural number because it is not finite and a natural number is finite. If it was a natural number, then N would not have a total ordering. I am becoming more and more an ultra-finitist. Arguments with infinity seem to be very based on the assumptions you make (about platonia or whatever) Finite and infinite concepts are dual concepts you can't leave one without leaving the other. Regards, Günther Regards, Quentin Anciaux -- All those moments will be lost in time, like tears in rain. --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: Cantor's Diagonal
Hi Russell, Russell Standish wrote: In your first case, the number (1,1,1,1...) is not a natural number, since it is infinite. In the second case, (0,0,0,...) is a natural number, but is also on the list (at infinity). Why is (1,1,1,...) not in the list but (0,0,0,...) in the list at infinity? This seems very arbitrary to me. I am becoming more and more an ultra-finitist. Arguments with infinity seem to be very based on the assumptions you make (about platonia or whatever) Regards, Günther -- Günther Greindl Department of Philosophy of Science University of Vienna [EMAIL PROTECTED] http://www.univie.ac.at/Wissenschaftstheorie/ Blog: http://dao.complexitystudies.org/ Site: http://www.complexitystudies.org --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
