Search results
Results from the WOW.Com Content Network
Symmetric and antisymmetric relations. By definition, a nonempty relation cannot be both symmetric and asymmetric (where if a is related to b, then b cannot be related to a (in the same way)). However, a relation can be neither symmetric nor asymmetric, which is the case for "is less than or equal to" and "preys on").
Peer relationships, such as can be governed by the Golden Rule, are based on symmetry, whereas power relationships are based on asymmetry. [35] Symmetrical relationships can to some degree be maintained by simple (game theory) strategies seen in symmetric games such as tit for tat. [36]
The symmetric group S n (on a finite set of n symbols) is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself. [4]
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 ...
A reflexive and symmetric relation is a dependency relation (if finite), and a tolerance relation if infinite. A preorder is reflexive and transitive. A congruence relation is an equivalence relation whose domain X {\displaystyle X} is also the underlying set for an algebraic structure , and which respects the additional structure.
For example, that every equivalence relation is symmetric, but not necessarily antisymmetric, is indicated by in the "Symmetric" column and in the "Antisymmetric" column, respectively. All definitions tacitly require the homogeneous relation R {\displaystyle R} be transitive : for all a , b , c , {\displaystyle a,b,c,} if a R b {\displaystyle ...
Symmetric relations contrast with non-symmetric relations, for which this pair-like behavior is not always observed. An example is the love-relation: if Dave loves Sara then it is possible but not necessary that Sara loves Dave. A special case of non-symmetric relations is asymmetric relations, which only go one way.
Symmetric difference = {: ()} is sometimes associated with exclusive or (xor) (also sometimes denoted by ), in which case if the order of precedence from highest to lowest is ,,, then the order of precedence (from highest to lowest) for the set operators would be , ,,.