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Similarly, a System F type has an inhabitant if and only if its corresponding proposition is a tautology of intuitionistic second-order logic. Girard's paradox shows that type inhabitation is strongly related to the consistency of a type system with Curry–Howard correspondence.
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 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.
A country demonym denotes the people or the inhabitants of or from there; for example, "Germans" are people of or from Germany. Demonyms are given in plural forms. Singular forms simply remove the final s or, in the case of -ese endings, are the same as the plural forms. The ending -men has feminine equivalent -women (e.g. Irishman, Scotswoman).
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 mathematical object is said to satisfy a property locally, if the property is satisfied on some limited, immediate portions of the object (e.g., on some sufficiently small or arbitrarily small neighborhoods of points).
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 ...
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).