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My description of the power set is by definition allowing all to imply some
by aabhay 2y ago
My description of the power set is by definition allowing all to imply some
- LudwigNagasena 2y agoI don’t follow. Can you elaborate?
- Spivak 2y agoThe power set of a set S, P(S) (or sometimes 2^S) is the set of all subsets of S including both the empty set and the set itself. To bridge the gap with programming, make a map f: S -> bool which represents our predicate. all(f, S) => either S is empty or for all elements s in S, f(s) = True. Now make f work on sets as well as individual values. f({x, y}) means True if f(x) and f(y) are True, False otherwise. all(f, S) => all(f, P(S)) If we take the opposite and define all(f, {}) = False then this doesn't work and in addition all(f, P(S)) = False for all sets S.
- LudwigNagasena 2y agoThat doesn’t explain how all(f,{}) => some(f,{}) may be made true with your definition preserving the distributive property.