Power Set of a Power Empty Set Find ℙ(ℙ(ℙ(∅))).
I know that ℙ(∅) = {∅}.
Then, ℙ(ℙ(∅)) = {∅, {∅}, {∅,{∅}}?
so, ℙ(ℙ(ℙ(∅))) = {∅,{∅, {∅}, {∅,{∅}}}?
Is it? Will it be ok if someone explain to me this concept?

I think it's easier if you consider $P(\varnothing)$ to be a one-element set, say $\{1\}$. Then it's pretty clear that $P(P(\varnothing))$ has to be precisely $\{ \varnothing, \{1\}\}$. So $P(P(P(\varnothing))) = \{\varnothing, \{\varnothing\}, \{\{1\}\}, \{\varnothing, \{1\}\}\}$.
