if $A = \{\emptyset, \{\emptyset\}, \{\emptyset, \{\emptyset\}\}\}$ what is |A|

Question

zugzwang · Answer

I think it's 3

lgbasallote · Answer

why so?

zugzwang · Answer

I counted them?

lgbasallote · Answer

but they're null....

zugzwang · Answer

It's set of sets (of sets), it's actually making me dizzy o.O

zugzwang · Answer

Let U = {}
$$V = P(U) = \left\{ \emptyset \right\}$$
$$W = P(V) = \left\{ \emptyset, \left\{ \emptyset \right\} \right\}$$
$$X = P(W) = \left\{ \emptyset, \left\{ \emptyset \right\}, \ \left\{ \left\{ \emptyset \right\} \right\}, \ \left\{ \emptyset, \ \left\{ \emptyset \right\} \right\} \right\}$$
|X| = 4
Now it's just a matter of taking away {{Ø}} making the cardinality 3

lgbasallote · Answer

....you made it more complicated than it's supposed to be.....

zugzwang · Answer

Well, my simpler answer was... I counted them :)