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Philosophical Studies

Philosophy of Mathematics is an active branch of Philosophy addressing questions about the character of Mathematics, the conduct of mathematical inquiry, and the role of mathematical objects in describing empirical phenomena. As a form of philosophical inquiry, it examines the record of mathematical inquiry and poses...

Information Theory

This article develops the theory of relations in regard to its specifically combinatorial aspects. For a general discussion of the basic definitions, see the articles on binary relations and relations_in_mathematics. Relations fall into various types according to their specific properties, often as expressed in the axioms or...

Mathematics

In mathematics, a finitary boolean function is a function of the form f : Bk ? B, where B  {0, 1} is a boolean domain and where k is a nonnegative integer. In the case where k - 0, the “function” is simply a constant element of B. More generally, a function of the form f : X ? B, where X is an arbitrary set, is a boolean-valued function] (see below). If...

Mathematics

In Mathematics, the word null (from German null and Norwegian null, which is from Latin nullus, both meaning “zero”, or “none”)cite journal |title=“null” |journal=The Oxford English Dictionary, Draft Revision March 2004 |url= dictionary.oed.com |year=2004 |accessdate-2007-04-05 may or may not have a meaning different from zero. Sometimes the symbol ? is used to...

Mathematics

In logic and mathematics, a parametric operator Omega! with parameter alpha! in the parametric set Alpha! is a indexed_family of operators (Omegaalpha)Alpha = Omegaalpha : alpha in Alpha with index alpha! in the index set Alpha!. A multigrade operator Omega is a parametric operator with parameter k in the set N of non-negative integers. The application of a...

Mathematics

Other Languages : (中文 : 关系 (数学)) This article presents the generalized concept of a relation. For more basic presentations see the articles on binary relations and triadic relations. In mathematics, a finitary relation is defined by one of the formal definitions...

Mathematics

In mathematics, a binary relation (or a dyadic relation) is an arbitrary association of elements of one set with elements of another (perhaps the same) set. An example is the “divides” relation between the set of prime numbers P and the set of integers Z, in which every prime p is associated to every integer z that is a multiple of p. In this...

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