Question

if \(A = \{\emptyset, \{\emptyset\}, \{\emptyset, \{\emptyset\}\}\}\) what is |A|

Answer 1

I think it's 3

Answer 2

why so?

Answer 3

I counted them?

Answer 4

but they're null....

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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