What is the cardinality if A = { {}, {{}, {}}}?

Question

I am still confused about null sets. I'm pretty sure that {} is equivalent to 0 with a / on it. Please help me. I don't want to fail math. :(

Answer 1

|A|, or the cardinality of A, is 2. There are two discrete elements of A, the null set {}, and the set of null sets {{},{}}.

Answer 2

It is helpful to identify the elements. The commas in the outermost pair of braces separate the individual elements.

 

{ {} , {{},{}} }

 

Here, there are two elements which happen to be sets {} and {{},{}}. The cardinality is therefore 2.