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If you have a set that looks like $S_1 = \{0,1,2,3,4\}$ I understand the cardinality of the set is $5$.

What about if you have a set of sets so

$S_1=\{S_2,S_3,S_4\}$ where,

$S_2=\{1,2,3\}$

$S_3=\{1,2\}$

$S_4=\{1\}$.

For the cardinality of $S_1$ 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 $S_1$ so it would be $3$.

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    The set of the members of the members of $S$ is denoted $\cup S$ and is not often equal to $S$ and often has a different cardinal'2017-02-01

1 Answers 1

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