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

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James Waldby

Posts: 356
Registered: 1/27/11
Re: Countably Infinite Sets
Posted: Dec 28, 2012 3:53 PM
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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



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