Properties in Mathematics
In mathematical terminology, a property p defined for all elements of a set X is usually defined as a function p: X → {true, false}, that is true whenever the property holds; or equivalently, as the subset of X for which p holds; i.e. the set {x| p(x) = true}; p is its indicator function. It may be objected (see above) that this defines merely the extension of a property, and says nothing about what causes the property to hold for exactly those values.
Read more about this topic: Property (philosophy)
Famous quotes containing the words properties and/or mathematics:
“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 three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.”
—Willard Van Orman Quine (b. 1908)