[Math] the cardinality of the set of the empty set

Question

Given set $ A = \{ \emptyset \}$ what is $|A|$? I just learned about sets today in class and I'm unsure how to answer this.

Answer 1

$A=\{\emptyset\}$ is a set containing one element. That element is itself also a set, but this is irrelevant.

Note the difference between $A=\{\emptyset\}$, $B=\emptyset$, and $C=\{\{\emptyset\}\}$. These are all different sets. $A$ is the set containing the emptyset. $B$ is the emptyset, and $C$ is the set containing the set containing the empty set.

Cardinality of a finite set is simply the number of elements contained in the set, so in this case $|A|=1$

Similarly, $|C|=1$ and $|B|=0$ for the other examples I added above.