In number theory, a rational point is a point in space each of whose coordinates are rational; that is, the coordinates of the point are elements of the field of rational numbers, as well as being elements of larger fields that contain the rational numbers, such as the real numbers and the complex numbers.
For example, (3, −67/4) is a rational point in 2 dimensional space, since 3 and −67/4 are rational numbers. A special case of a rational point is an integer point, that is, a point all of whose coordinates are integers. E.g., (1, −5, 0) is an integral point in 3-dimensional space. On the other hand, more generally, a K-rational point is a point in a space where each coordinate of the point belongs to the field K, as well as being elements of larger fields containing the field K. This is analogous to rational points, which, as stated above, are contained in fields larger than the rationals. A corresponding special case of K-rational points are those that belong to a ring of algebraic integers existing inside the field K.
Read more about Rational Point: Rational or K-rational Points On Algebraic Varieties, Rational Points of Schemes, See Also
Famous quotes containing the words rational and/or point:
“There has never been in history another such culture as the Western civilization M a culture which has practiced the belief that the physical and social environment of man is subject to rational manipulation and that history is subject to the will and action of man; whereas central to the traditional cultures of the rivals of Western civilization, those of Africa and Asia, is a belief that it is environment that dominates man.”
—Ishmael Reed (b. 1938)
“The tabloids are like animals, with their own behavioural patterns. There’s no point in complaining about them, any more than complaining that lions might eat you.”
—David Mellor (b. 1949)