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Prove the existence of infinite number of infinite cardinals

1) $\alpha$, such that $\alpha<\alpha^\aleph$

2) $\beta$, such that $\beta=\beta^\aleph$

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    You might want to look at http://meta.math.stackexchange.com/questions/1803/how-to-ask-a-homework-question for some tips on asking questions here (even if this isn't homework).2012-04-19

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