Power Set
The power set is the set consisting of all subsets of .
Example
If , then .
No universal set
The expression cannot be formed for arbitrary properties . Suppose were a set: if then by definition , while if then by construction. There is therefore no universal set with for all ; otherwise could be formed as . A set is guaranteed to exist when it is obtained from known sets such as or by the constructions above.
Related
Stated in
- Definition 2.8 (Power Set)§2.1.2 Properties of Sets