I know that we can easily construct a set whose cardinality is strictly greater than that of the set of real numbers by taking P([itex]\Re[/itex]) where P denotes the power-set operator. But as far as I am aware there aren't really any uses for this class of sets (up to bijection), or any intuitive ways of graphically representing them.(adsbygoogle = window.adsbygoogle || []).push({});

Does anyone know of any sets whose cardinalities are [itex]\aleph_2[/itex], [itex]\aleph_3[/itex] etc. that have actually been useful in proofs?

I am somewhat math-literate (undergraduate degree in math) but I would really appreciate simple, easily thought-about examples if any exist.

Thanks

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# Set whose cardinality is [itex]\aleph_2[/itex]?

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