How would we prove that infinite sets have at least a cardinality of aleph naught?
All infinite sets have a cardinality of at least aleph naught
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discrete-mathematics
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0This is the definition of $\aleph_0$, no? The smallest infinite cardinal. – 2012-09-30
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0How would we prove the definition? – 2012-09-30
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2What are your definitions of "infinite" and "aleph naught"? – 2012-09-30
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0"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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1This 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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0I recall writing an answer a few days ago. – 2012-09-30
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0@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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0@Martin: Yes. I suppose. I am also certain that this question has been answered uncountably many times on this site before. – 2012-09-30