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I get the basic concept of set cardinality. For example if you have $A = \{3, 4, 5, 6\}$, the set cardinality would be $4$.

What I don't grasp is problems like: $A = \{a, a \{b, a \{a \}\}\}$ or $A = \{a\}$

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    Are there a few commas missing in the first example? Shouldn't it be $A=\{a,a,\{b,a,\{a\}\}\}$?2012-10-23
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    You count the things that are inside the set, not the things inside of the things inside of the set. $\{a,b,\{c,d\}\}$ has cardinality of 3, not 4 (its elements are $a$, $b$, and $\{c,d\}$).2012-10-23
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    ... assuming $a \neq b$ and $a \neq \{c,d\}$ and $b \neq \{c, d\}$.2012-10-23

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