Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Countably Infinite Sets
Replies: 11   Last Post: Dec 28, 2012 9:08 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
ross.finlayson@gmail.com

Posts: 1,214
Registered: 2/15/09
Re: Countably Infinite Sets
Posted: Dec 27, 2012 10:02 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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?




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.