Virgil
Posts:
8,833
Registered:
1/6/11


Re: Countably Infinite Sets
Posted:
Dec 28, 2012 8:19 PM


In article <kbl0sv$n1u$2@dontemail.me>, James Waldby <not@valid.invalid> wrote:
> 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.
Do you mean S is orderisomorphic to N?. 

