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/
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