Le 22-nov.-07, à 07:19, Barry Brent a écrit :
>
> The reason it isn't a bijection (of a denumerable set with the set of
> binary sequences): the pre-image (the left side of your map) isn't
> a set--you've imposed an ordering. Sets, qua sets, don't have
> orderings. Orderings are extra. (I'm not a specialist on this stuff
> but I think Bruno, for example, will back me up.) It must be the
> case that you won't let us identify the left side, for example, with
> {omega, 0, 1, 2, ... }, will you? For if you did, it would fall under
> Cantor's argument.
I agree.
Presently, I prefer not talking too much on the ordinals, because it
could be confusing for many. More later ...
Bruno
http://iridia.ulb.ac.be/~marchal/
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