Power Set

P (A)

Let $A$ be a set. Then $P (A)$ is the power set of $A$ where $P = {B | B \subseteq A}$ .

For example, if $A = {1, 2}$ then:

P (A) = {\emptyset, {1}, {2}, {1, 2}}

Notice that always both $\emptyset, A \in P (A)$ .

\emptyset \neq {\emptyset}

With finite sets it's pretty controlled what happens:

A

is finite with

n

elements, then

P (A)

has

2^{n}

elements.