Date: Dec 28, 2012 3:53 PM
Author: James Waldby
Subject: Re: Countably Infinite Sets

On Fri, 28 Dec 2012 12:51:29 -0600, fasnsto wrote:
> "netzweltler" <reinhard_fischer@arcor.de> wrote ...
>> Does the set {{1}, {1,2}, {1,2,3}, ...} contain all natural numbers?
>
> no, it would contain the set of all natural numbers.


Let S = {{1}, {1,2}, {1,2,3}, ...}. The infinite union of the members
of S would be a set containing all natural numbers, but no member of S
is itself a set containing all natural numbers. Of course, as noted in
some earlier replies, S is isomorphic to the naturals.

--
jiw