Concept
Finitary relation
Overview
In mathematics, a finitary relation over a sequence of sets X1, ..., Xn is a subset of the Cartesian product X1 × ... × Xn; that is, it is a set of n-tuples (x1, ..., xn), each being a sequence of elements xi in the corresponding Xi. Typically, the relation describes a possible connection between the elements of an n-tuple. For example, the relation "x is divisible by y and z" consists of the set of triples such that when substituted to x, y and z, respectively, make the sentence true.
The non-negative integer n that gives the number of "places" in the relation is called the arity, adicity or degree of the relation. A relation with n "places" is variously called an n-ary relation, an n-adic relation or a relation of degree n. Relations with a finite number of places are called finitary relations (or simply relations if the context is clear). It is also possible to generalize the concept to infinitary relations with infinite sequences.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
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Two sets of four points each are defined as having the same anharmonic ratio, when (1) each set of four lies in one straight line, and (2) corresponding points of different sets lie two by two on four straight lines through a single point, or when both sets have this relation to any third set[123]. And reciprocally: Two sets of four straight lines are defined as having the same anharmonic ratio when (1) each set of…
Bertrand Russell, An essay on the foundations of geometry
States what Finitary relation is; the author is tied to Finitary relation in the knowledge graph.
All types of series are capable of formal definition, and their properties can be deduced from the principles of symbolic logic by means of the Algebra of Relatives. The notion of a limit, which is fundamental in the greater part of higher mathematics, used to be defined by means of quantity, as a term to which the terms of some series approximate as nearly as we please. But nowadays the limit is defined quite…
Bertrand Russell, Mysticism and Logic and Other Essays
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Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.
Alfred North Whitehead, Science and the modern world
States what Finitary relation is.
Philosophers who discussed Finitary relation
Related ideas
- Georg Cantor
- Tuple
- Interpretation (logic)
- Intension
- The Principles of Mathematics
- Mathematics
- Mathematical induction
- Augustus De Morgan
- Model theory
- Nobel Prize
- Richard Dedekind
- Applied mathematics
- Polish notation
- Statistics
- Set theory
- Subset
- Partition of a set
- Boolean domain
- Bertrand Russell
- Arity
- Logic
- Gottlob Frege
- Computer science
- Charles Sanders Peirce
Place in the tradition
Part of First-order logic.