Search results
Results From The WOW.Com Content Network
In mathematics, a finitary relation over a sequence of sets X 1, ..., X n is a subset of the Cartesian product X 1 × ... × X n; that is, it is a set of n-tuples (x 1, ..., x n), each being a sequence of elements x i in the corresponding X i. [1] [2] [3] Typically, the relation describes a possible connection between the elements of an n-tuple.
In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...
In mathematics and logic, an operation is finitary if it has finite arity, i.e. if it has a finite number of input values. Similarly, an infinitary operation is one with an infinite number of input values. In standard mathematics, an operation is finitary by definition. Therefore, these terms are usually only used in the context of infinitary ...
A finitary or n-ary relation is a set of n-tuples. Specific types of relations include: Relation (mathematics) (an elementary treatment of binary relations) Binary relation (or diadic relation – a more in-depth treatment of binary relations) Equivalence relation; Homogeneous relation; Reflexive relation; Serial relation
In mathematics, an operation is a function from a set to itself. For example, an operation on real numbers will take in real numbers and return a real number. An operation can take zero or more input values (also called "operands" or "arguments") to a well-defined output value.
In mathematics, a ternary relation or triadic relation is a finitary relation in which the number of places in the relation is three. Ternary relations may also be referred to as 3-adic, 3-ary, 3-dimensional, or 3-place.
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it.. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces.
The Ackermann coding can be used to construct a model of finitary set theory in the natural numbers. More precisely, ( N , BIT ⊤ ) {\displaystyle (\mathbb {N} ,{\text{BIT}}^{\top })} (where BIT ⊤ {\displaystyle {\text{BIT}}^{\top }} is the converse relation of BIT {\displaystyle {\text{BIT}}} , swapping its two arguments) models Zermelo ...