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

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 netzweltler Posts: 473 From: Germany Registered: 8/6/10
Re: Countably Infinite Sets
Posted: Dec 28, 2012 5:16 PM

On 28 Dez., 21:53, James Waldby <n...@valid.invalid> wrote:
> On Fri, 28 Dec 2012 12:51:29 -0600, fasnsto wrote:
> > "netzweltler" <reinhard_fisc...@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

I understand, that the union of the members of S contains all natural
numbers. But, did I really write the union here?
{{1}, {1,2}, {1,2,3}, ...}

Isn't it a list of infinitely many rows like

1
1,2
1,2,3
...

Does the list contain all natural numbers? Is this list an union?

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