find $P\{P\{0\}\}$. $P$ represents the power set. I'm assuming that I'm trying to find the power set of a power set?
I start from the inner power set, $P\{0\}$. $P\{0\}= \{ 0, \{0\} \}$.
Now I do $P\{ 0, \{0\} \}$ which is $\{ 0, \{0\}, \{\{0\}\} \}$.
0 is the empty set.
Is this correct?
So I'm taking it that P{0}={0, {0}, {0, {0}} }

You've forgotten $\{0,\{0\}\}$ as an element of $P(0)$.
