Re: Cantor Confusion

In article <1166092856.281805.315200@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

Virgil schrieb:


One can define such functions called sequences, but that does not
guarantee that all the pairs do actually exist. The pair (x, f(x)) with
x = floor(pi*10^10^100) does not exist, for instance.

If f(x) = 1 for all x then the pair (x,1) exists for all x.

No. The pair (x,1) exists only for all those x which exist.

But what do you mean and understand by "to exist"? In *every* set
theory, starting from Cantor, it means to exist actually.

I am not aware of any set theory in which any set is declared to
"actually" exist, though there are those in which sets are declared to
exist.

You are not aware of many things in set theory.

Possibly.


But many of the things WM declares a part of his set theory are not any
part of any standard set theory and many of the things in standard set
theories are not parts do WM's set theory.

And Wm has not presented an axiom system for his own set theory, so no
one else can tell what it actually does say.

So I will stick with the standards.


If Cantor's list does not actually exist

Then Cantor's first proof is still valid.
.

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