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If you have a set that looks like S1 = {0,1,2,3,4} I understand the cardinality of the set is 5.

What about if you have a set of sets so

S1 = {S2, S3, S4}
S2 = {1, 2, 3} 
S3 = {1, 2}
S4 = {1}

For the cardinality of S1 do you count all the elements of the included sets so the answer would be 6 or do you just count the number in the S1 so it would be 3

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up vote 3 down vote accepted

It is the latter, i.e. we just count the number of elements of $S1$, which is 3.

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