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:
“We fetch fire and water, run about all day among the shops and markets, and get our clothes and shoes made and mended, and are the victims of these details, and once in a fortnight we arrive perhaps at a rational moment.”
—Ralph Waldo Emerson (1803–1882)
“No one can doubt the purpose for which the Nation now seeks to use the Democratic Party. It seeks to use it to interpret a change in its own plans and point of view.”
—Woodrow Wilson (1856–1924)