Date: Dec 27, 2012 10:02 PM
Author: ross.finlayson@gmail.com
Subject: Re: Countably Infinite Sets

On Dec 27, 6:56 pm, William Elliot <ma...@panix.com> wrote:
> On Thu, 27 Dec 2012, netzweltler wrote:
> > Does the set {{1}, {1,2}, {1,2,3}, ...} contain all natural numbers?
>
> No, it contains subsets of N, the set of positive integers.
>
> On the other hand, the great union of your set is N.


Some might have those sets, as ordinals, being the elements of N, in
constructing the naturals with the Peano axioms.

Otherwise though you're quite right those are initial segments of N,
or, the elements of those initial segments, with its normal ordering.

Some have the direct sum of those being N, others, empty.

What does "..." mean?