Power Set/Examples/Nested Sets of Empty Sets
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Example of Power Set
Let $\O$ denote the empty set.
Let $S$ be the set defined as:
- $S = \set {\O, \set \O, \set {\set \O} }$
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.
Sources
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 2$. Sets of sets: Exercise $2$