
Re: Countably Infinite Sets
Posted:
Dec 28, 2012 3:53 PM


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

