[FOM] FOM Cantor's argument

[Giuseppina Ronzitti]

Neil Tennant wrote:

> The quick answer to your concerns is that one can prove Cantor's Theorem:
>
> "for every set X there is no many-one relation mapping X onto all subsets
> of X"

I am sorry I am not able to understand  the use of the locution "there is no
function from X onto *all subsets * of X". Onto *what* ? Would you write
something like: f : X ---> *all subsets of X* ?


> in a form that does NOT presuppose or entail the existence of the power
> set of X.
>
> To get the "onto" condition expressed without commitment to the power set,
> simply write
>
>    for every subset Y of X, there is a member x of X such that R(x,Y);
>

*for every subset Y of X*,  to my understanding,  means  *for every object Y in
P(X)*.


G. Ronzitti
Genova, Italy
Europe