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

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Virgil

Posts: 6,972
Registered: 1/6/11
Re: Countably Infinite Sets
Posted: Dec 28, 2012 8:19 PM
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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?.
--





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