Power Set/Examples/Axiomatic Definition of 2

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

Let $S$ be the set defined as the $2$nd element of the von Neumann construction of the natural numbers:


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

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

and so has $2^2 = 4$ elements.