# Power set

1. Oct 4, 2013

1. The problem statement, all variables and given/known data

How many elements does this set have?

* P(P(∅))

2. Relevant equations

I know that if a set has n elements, then its power set has 2^n elements but i really want to know if (P(∅)) is just one element or not.

2. Oct 4, 2013

### jbunniii

How many subsets does $\emptyset$ have?

3. Oct 4, 2013

### Dick

Sure it is. The empty set has one subset. Itself. But remember P is the SET of subsets. So P(∅) isn't ∅. It's {∅}. There is a difference.