Properties
- The complement of an arithmetical set is an arithmetical set.
- The Turing jump of an arithmetical set is an arithmetical set.
- The collection of arithmetical sets is countable, but there is no arithmetically definable sequence that enumerates all arithmetical sets.
- The set of real arithmetical numbers is denumerable, dense and order-isomorphic to the set of rational numbers.
Read more about this topic: Arithmetical Set
Famous quotes containing the word properties:
“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)
“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)