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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Countably Infinite Sets
Replies: 11   Last Post: Dec 28, 2012 9:08 PM

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Butch Malahide

Posts: 885
Registered: 6/29/05
Re: Countably Infinite Sets
Posted: Dec 27, 2012 10:08 PM
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On Dec 27, 8:43 pm, netzweltler <reinhard_fisc...@arcor.de> wrote:
> Does the set {{1}, {1,2}, {1,2,3}, ...} contain all natural numbers?

No, because it does not contain the natural number 1; if it did, then
1 would be an element of itself, contradiction the axiom of regularity.

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