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How would we prove that infinite sets have at least a cardinality of aleph naught?

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    This is the definition of $\aleph_0$, no? The smallest infinite cardinal.2012-09-30
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    How would we prove the definition?2012-09-30
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    What are your definitions of "infinite" and "aleph naught"?2012-09-30
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    "infinite" set means there are an infinite number of elements in the set. "aleph naught" means the cardinality of the natural numbers.2012-09-30
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    This seems related: [Why is $\omega$ the smallest $\infty$?](http://math.stackexchange.com/questions/10085/why-is-omega-the-smallest-infty)2012-09-30
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    I recall writing an answer a few days ago.2012-09-30
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    @Asaf Do you mean this question? [Infinite set and countable subset](http://math.stackexchange.com/questions/203083/infinite-set-and-countable-subsets)2012-09-30
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    @Martin: Yes. I suppose. I am also certain that this question has been answered uncountably many times on this site before.2012-09-30

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