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His usage is correct.

Cardinality refers to the size of any set. This includes finite, countable, and uncountable sets.

The sequence of cardinal numbers is transfinite: 0, 1, 2, ... , n, ..., aleph_0, aleph_1, ...

http://en.wikipedia.org/wiki/Cardinality

http://en.wikipedia.org/wiki/Cardinal_number



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