Re: Cantor Confusion

Albrecht wrote:
The idea of "all infinite many objects" in any sense is
self-contradicting. There is no "all" of infinite many things.


Han de Bruijn wrote:
Bravo! Another mathematician (?) who cares about disciplinary thinking.

Let's see. If I define set N as containing "all" of the naturals, i.e.,
{0,1,2,3,...}, you're (both) saying that N can't exist as a real set,
because there is no way to have "all" of an "infinitely many" elements
at once.

So then we must conclude that there are naturals that are not in N,
because N can't contain all the (infinitely many) naturals.

So now I define another set N' to contain all the naturals except those
that are already in N, i.e., those naturals that we concluded must be
omitted from N.

So what is in this second set N'? Is it also not an infinite set?

.

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