Solving the Mystery of P(P(∅))

[Madonna M.]

1. Homework Statement

How many elements does this set have?

* P(P(∅))

2. Homework 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.

Thanks in advance..

 

[jbunniii]

How many subsets does $\emptyset$ have?

 

[Dick]

1. Homework Statement

How many elements does this set have?

* P(P(∅))

2. Homework 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.

Thanks in advance..

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.