Properties
A set X is transitive if and only if, where is the union of all elements of X that are sets, . If X is transitive, then is transitive. If X and Y are transitive, then X∪Y∪{X,Y} is transitive. In general, if X is a class all of whose elements are transitive sets, then is transitive.
A set X which does not contain urelements is transitive if and only if it is a subset of its own power set, The power set of a transitive set without urelements is transitive.
Read more about this topic: Transitive Set
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)