Full Idea
The Power Set is just he codification of the fact that the collection of functions from a mathematical collection to a mathematical collection is itself a mathematical collection that can serve as a domain of mathematical study.
Gist of Idea
The Power Set is just the collection of functions from one collection to another
Source
Shaughan Lavine (Understanding the Infinite [1994], VI.1)
Book Reference
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.160