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Generalization
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==Examples== ===Biological generalization=== [[File:Generalization process using trees.svg|thumb|right|alt=Diagram|When the mind makes a generalization, it extracts the essence of a concept based on its analysis of similarities from many discrete objects. The resulting simplification enables higher-level thinking.]] An animal is a generalization of a [[mammal]], a bird, a fish, an [[amphibian]] and a reptile. ===Cartographic generalization of geo-spatial data=== {{Main|Cartographic generalization}} 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.<ref>{{Cite web|url=https://www.axismaps.com/guide/general/scale-and-generalization/|title=Scale and Generalization|date=14 October 2019|website=Axis Maps|access-date=30 November 2019}}</ref> 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 {{mvar|B}} is a ''generalization'' of {{mvar|A}} if {{mvar|A}} is defined or proved before {{mvar|B}} (historically or conceptually) and {{mvar|A}} is a special case of {{mvar|B}}. * 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 [[Variable (mathematics)|''n'']] sides. * A [[hypercube]] is a generalization of a 2-dimensional square, a 3-dimensional [[cube]], and so on to ''n'' [[dimension]]s. * 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 <math>(1+x)^n</math>. * A [[ring (mathematics)|ring]] is a generalization of a [[field (mathematics)|field]].
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