Relation[]
The Arithmetic field of study covers any activity that studies Arithmetic in order to manifest the material. The Algebra field of study covers any activity that studies Algebra in order to manifest the material. In mathematics, especially set theory, and logic, a relation is a property that assigns truth values to combinations (k-tuples) of k individuals. Typically, the property describes a possible connection between the components of a k-tuple. For a given set of k-tuples, a truth value is assigned to each k-tuple according to whether the property does or does not hold.
An example of a ternary or triadic relation (i.e., between three individuals) is: "X was-introduced-to Y by Z", where (X,Y,Z) is a 3-tuple of persons; for example, "Beatrice Wood was-introduced-to Henri-Pierre Roché by Marcel Duchamp" is true, while "Karl Marx was-introduced-to Friedrich Engels by Queen Victoria" is false.
The variable k giving the number of "places" in the relation, 3 for the above example, is a non-negative integer (zero, one, two, ...), called the relation's arity, adicity, or dimension. A relation with k places is variously called a k-ary, a k-adic, or a k-dimensional relation. Relations with a finite number of places are called finite-place or finitary relations. It is possible to generalize the concept to include infinitary relations between infinitudes of individuals, for example infinite sequences; however, in this article only finitary relations are discussed, which will from now on simply be called relations.