User:Ascii/Prose Test/Set Theory 2

Sets and Elements

The subset relation is reflexive; that is, every set is a subset of itself. The singleton of an element of a set is a subset of that set. The subset relation is transitive; that is, if a set is a subset of a second and the second is a subset of a third, the first is a subset of the third. Sets are equal iff they are subsets of each other. A set equals itself. Sets are unequal if neither is a subset of the other. The empty set is unique, a subset of all sets, and an element of every power set. A set is an element of its power set. The power set of the empty set is the singleton of the empty set.