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 $A = \{a\}$
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 $A = \{a\}$
You just count how many separate things there are in the set. Whether these things are subsets, symbols, functions or whatever doesn't matter. Each thing counts as one. Thus,
To test whether two sets are equal, you have to check whether they contain exactly the same things. If every thing contains in $A$ is also contained in $B$, and the other way round, then (and only then) are $A$ and $B$ equal.