Date: Jun 21, 2013 3:29 AM
Subject: Re: WMytheology § 293

Re: WMytheology § 293
In article
WM <> wrote:

> On 19 Jun., 23:38, Virgil <> wrote:

> The union of all of {1}, {1,2}, {1,2,3}, ...accomplishes
exactly the same as the union of all of {1}, {2}, {3}, ...,


> No more and no less, absolutely everywhere


> But, abracadabra, if you union the results of infinitely many unions,
> then you get the missing aleph_0 numbers.

If anyone but WM unions all infinitely many sets {1}, {2}, {3}, ...,
they get |N, and since every one of the infinitely many sets,
{1}, {1,2}, {1,2,3}, ... is a proper subset of |N, unioning all of them cannot give any more than |N.

Certainly not more, but a lot less.

The sequence of sets is inclusion-monotonic. This means there are never two or more sets the union of which surpasses each of the sets.

The sequence contains only sets each of which lack aleph_0 natural numbers.
Lacking infinitely many natural numbers cannot be compensated by unioning infinitely many of such deficient sets.

That's the reason why FredJeffries wished to prohibit the union of a sequence of sets.
Unfortunately his desire cannot be granted.

Regards, WM