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i realize that there are multiple sizes of infinity so one can be larger than another, but how do you show that one infinity is larger. I'm not looking for proofs or anything but I just want the notation that would be used in a problem or anything. I read something about alphas and omegas to distinguish the sizes of infinity but I can't find any explanations.

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    In this context (comparison of cardinals) we just use "<". For example, $\aleph_0 < 2^{\aleph_0}$. The first is the cardinality of the natural numbers, the second is the cardinality of the real numbers.2011-05-16
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    Look here: http://en.wikipedia.org/wiki/Aleph_number and here: http://en.wikipedia.org/wiki/Ordinal_number (if you just want "sizes of infinity", you're probably looking for the former).2011-05-16

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