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In Mathematics, the cardinality of a set is the number of elements it contains.
So the cardinality of {3, 7, 11, 15, 99} is 5.
The cardinality of {2, 4, 6, 8, 10, 12} is 6.
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That is all very well for finite sets. But many common sets are infinite: integers, rationals, reals.
The cardinality of all of these sets is infinity, but they are of two "levels" of infinity. Integers and rationals, for example have a cardinality of Aleph-null whereas irrationals and reals have a cardinality of aleph-one. It has been shown that there are no sets of cardinality between Aleph-null and Aleph-one.
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