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.

Sources

• 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 2$. Sets of sets: Exercise $2$