Power Set/Examples/Nested Sets of Empty Sets

Example of Power Set
Let $\O$ denote the empty set.

Let $S$ be the set defined as the union $2$nd element of the minimal infinite successor set:


 * $S = \set {\O, \set \O, \set {\set \O} }$

Then the power set of $S$ is:
 * $\powerset S = \set {\O, \set \O, \set {\set \O}, \set {\set {\set \O} }, \set {\O, \set \O}, \set {\O, \set {\set \O} }, \set {\set \O, \set {\set \O} }, \set {\O, \set \O, \set {\set \O} } }$

and so has $2^3 = 8$ elements.