Corollary: We already know that the functions from $ A $ to $ 2 $ form a set, $ 2^A $ . When we are thinking of $ 2^A $ as the set of all subsets of $ A $ , we call it the power set of $ A $ and write it as $ \pset(A) $ . \paragraph*{Equalizers} It would be nice if, given a set $ A $ , we could define a subset $ S $ of $ A $ by specifying a property that the elements of $ S $ are to satisfy: