Search All of the Math Forum:

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Countably Infinite Sets
Replies: 7   Last Post: Dec 29, 2012 12:45 PM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Countably Infinite Sets
Posted: Dec 28, 2012 8:19 PM

In article <kbl0sv\$n1u\$2@dont-email.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 order-isomorphic to |N?.
--

Date Subject Author
12/28/12 James Waldby
12/28/12 netzweltler
12/28/12 Virgil
12/28/12 James Waldby
12/29/12 netzweltler
12/29/12 Scott Berg