Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Matheology § 293
Replies: 44   Last Post: Jun 27, 2013 2:25 PM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: WMytheology § 293
Posted: Jun 21, 2013 3:29 AM

Re: WMytheology § 293
In article
WM <muec...@rz.fh-augsburg.de> wrote:

> On 19 Jun., 23:38, Virgil <vir...@ligriv.com> 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}, ...,

Yes.

> No more and no less, absolutely everywhere

Yes.

>
> 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