The cardinal number of a set is the number of objects in the set.
http://mathoverflow.net/questions/22243/what-is-the-smallest...
Cardinal Number.— The cardinal number, then, of an assemblage a is something that is common to all the assemblages similar to a, or as we shall say, since classes are more amenable to mathematical treatment than properties, the class of all assemblages similar to a. We shall represent cardinal numbers by the letters ', P, V. ir, P, and the cardinal number of the as semblage a by the symbol Nc 'a. It may be shown that our ordinary 0 is en,and that l is Nc' ex, or the class of all the classes ex.
http://gluedideas.com/content-collection/encyclopedia-americ...

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Note added at 38 mins (2012-02-06 09:21:35 GMT)
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Def. Set. Any collection of objects.

No restriction is placed on the nature of the objects in a set. They can be anything: points, lines, numbers, people, countries, etc. Thus the mathematical meaning of the word set is the same as the regular, nontechnical meaning of the word.
Cardinal number of a set. Two sets are said to have the same cardinal number if and only if they can be put into one-to-one correspondence i.e. if and only if they are equivalent.
A set A is said to have the cardinal number n if and only if there exists a one-to-one correspondence between the elements of A and the natural numbers 1, 2, 3, .... , n.

Synonyms. The cardinal number of a set is also called the potency of the set or power of the set.
http://www.solitaryroad.com/c725.html