Search results
Results From The WOW.Com Content Network
A function that is injective. For example, the green relation in the diagram is an injection, but the red, blue and black ones are not. A surjection [d] A function that is surjective. For example, the green relation in the diagram is a surjection, but the red, blue and black ones are not. A bijection [d] A function that is injective and surjective.
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...
A relation R is called intransitive if it is not transitive, that is, if xRy and yRz, but not xRz, for some x, y, z. In contrast, a relation R is called antitransitive if xRy and yRz always implies that xRz does not hold. For example, the relation defined by xRy if xy is an even number is intransitive, [13] but not antitransitive. [14]
In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation.The motivating example of a relation algebra is the algebra 2 X 2 of all binary relations on a set X, that is, subsets of the cartesian square X 2, with R•S interpreted as the usual composition of binary relations R and S, and with the ...
Another form of composition of relations, which applies to general -place relations for , is the join operation of relational algebra. The usual composition of two binary relations as defined here can be obtained by taking their join, leading to a ternary relation, followed by a projection that removes the middle component.
In Mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.
For example, if the function f is defined as (,) = + then is a symmetric function. For relations, a symmetric relation is analogous to a commutative operation, in that if a relation R is symmetric, then .
For example, a group is a set with an associative operation, often called multiplication, with an identity element, such that every element has an inverse element. Here, the auxiliary operations are the nullary operation that results in the identity element and the unary operation of inversion. A subset of a group that is closed under ...