Imaginary Point
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 Imaginary Point: Rational or K-rational Points On Algebraic Varieties, Rational Points of Schemes
Famous quotes containing the words imaginary and/or point:
“Avarice, the spur of industry, is so obstinate a passion, and works its way through so many real dangers and difficulties, that it is not likely to be scared by an imaginary danger, which is so small that it scarcely admits of calculation.”
—David Hume (1711–1776)
“By many a legendary tale of violence and wrong, as well as by events which have passed before their eyes, these people have been taught to look upon white men with abhorrence.... I can sympathize with the spirit which prompts the Typee warrior to guard all the passes to his valley with the point of his levelled spear, and, standing upon the beach, with his back turned upon his green home, to hold at bay the intruding European.”
—Herman Melville (1819–1891)