Le 21-nov.-07, à 17:33, Torgny Tholerus a écrit : > What do you think of this "proof"?: > > Let us have the bijection: > > 0 -------- {0,0,0,0,0,0,0,...} > 1 -------- {1,0,0,0,0,0,0,...} > 2 -------- {0,1,0,0,0,0,0,...} > 3 -------- {1,1,0,0,0,0,0,...} > 4 -------- {0,0,1,0,0,0,0,...} > 5 -------- {1,0,1,0,0,0,0,...} > 6 -------- {0,1,1,0,0,0,0,...} > 7 -------- {1,1,1,0,0,0,0,...} > 8 -------- {0,0,0,1,0,0,0,...} > ... > omega --- {1,1,1,1,1,1,1,...} > > What do we get if we apply Cantor's Diagonal to this?

Note also that in general, we start from what we want to prove, and then do the math. Your idea of transfinite (ordinal) diagonalisation is cute though, but I have currently no idea where this could lead. BTW, it is also funny that such a transfinite idea is proposed by an ultrafinistist! I guess you have seen that {(0,0,0,0,0,0,0,...), (1,0,0,0,0,0,0,...), ... does clearly not enumerate the infinite sequences (you don't have to use the diagonal for showing that. It is also better to use parentheses instead of accolades, given that the binary sequences are ordered (notation detail). Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---