netzweltler
Posts:
278
From:
Germany
Registered:
8/6/10
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Re: Countably Infinite Sets
Posted:
Dec 28, 2012 5:16 PM
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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?
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