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Examples include the class of all groups, the class of all vector spaces, and many others. In category theory, a category whose collection of objects forms a proper class (or whose collection of morphisms forms a proper class) is called a large category. The surreal numbers are a proper class of objects that have the properties of a field.
In constructive mathematics, "not empty" and "inhabited" are not equivalent: every inhabited set is not empty but the converse is not always guaranteed; that is, in constructive mathematics, a set that is not empty (where by definition, "is empty" means that the statement () is true) might not have an inhabitant (which is an such that ).
The following is a list of adjectival forms of cities in English and their demonymic equivalents, which denote the people or the inhabitants of these cities. Demonyms ending in -ese are the same in the singular and plural forms. The ending -man has feminine equivalent -woman (e.g. an Irishman and a Scotswoman).
The equivalence class of a set A under this relation, then, consists of all those sets which have the same cardinality as A. There are two ways to define the "cardinality of a set": The cardinality of a set A is defined as its equivalence class under equinumerosity. A representative set is designated for each
The interior of a point in an at least one-dimensional ambient space is empty, but its relative interior is the point itself. The interior of a line segment in an at least two-dimensional ambient space is empty, but its relative interior is the line segment without its endpoints.
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures.Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships existing among the representing objects y i conform, in some consistent way, to ...
Geodemography is the study of people based on where they live [citation needed]; it links the sciences of demography, the study of human population dynamics, and geography, the study of the locational and spatial variation of both physical and human phenomena on Earth, [1] along with sociology.