# Re: Cantor's Diagonal

```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
ordered (notation detail).

Bruno

http://iridia.ulb.ac.be/~marchal/

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