Higher Cardinals: Example of Set with Cardinality Aleph2?

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Just an ideal question, possibly asked before, but is there an example of a Set which has cardinality of \aleph_{2}?
 
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That's a tough one, since it depends on the assumptions you use. With the GCH, the set of all functions f:\mathbb{R}\rightarrow\mathbb{R} has cardinality \aleph_2.
 

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