Generalization

The connection of generalization to specialization (or particularization) is reflected in the contrasting words hypernym and hyponym. A hypernym as a generic stands for a class or group of equally ranked items, such as the term tree which stands for equally ranked items such as peach and oak, and the term ship which stands for equally ranked items such as cruiser and steamer. In contrast, a hyponym is one of the items included in the generic, such as peach and oak which are included in tree, and cruiser and steamer which are included in ship. A hypernym is superordinate to a hyponym, and a hyponym is subordinate to a hypernym. ==Examples==

Biological generalization An animal is a generalization of a mammal, a bird, a fish, an amphibian and a reptile. Cartographic generalization of geo-spatial data Generalization has a long history in cartography as an art of creating maps for different scale and purpose. Cartographic generalization is the process of selecting and representing information of a map in a way that adapts to the scale of the display medium of the map. In this way, every map has, to some extent, been generalized to match the criteria of display. This includes small cartographic scale maps, which cannot convey every detail of the real world. As a result, cartographers must decide and then adjust the content within their maps, to create a suitable and useful map that conveys the geospatial information within their representation of the world. Generalization is meant to be context-specific. That is to say, correctly generalized maps are those that emphasize the most important map elements, while still representing the world in the most faithful and recognizable way. The level of detail and importance in what is remaining on the map must outweigh the insignificance of items that were generalized—so as to preserve the distinguishing characteristics of what makes the map useful and important. Mathematical generalizations In mathematics, one commonly says that a concept or a result is a generalization of if is defined or proved before (historically or conceptually) and is a special case of . • The complex numbers are a generalization of the real numbers, which are a generalization of the rational numbers, which are a generalization of the integers, which are a generalization of the natural numbers. • A polygon is a generalization of a 3-sided triangle, a 4-sided quadrilateral, and so on to n sides. • A hypercube is a generalization of a 2-dimensional square, a 3-dimensional cube, and so on to n dimensions. • A quadric, such as a hypersphere, ellipsoid, paraboloid, or hyperboloid, is a generalization of a conic section to higher dimensions. • A Taylor series is a generalization of a MacLaurin series. • The binomial formula is a generalization of the formula for (1+x)^n. • A ring is a generalization of a field. ==See also==