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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 set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class. A collection F {\displaystyle F} of subsets of a given set S {\displaystyle S} is called a family of subsets of S {\displaystyle S} , or a family of sets over S ...
The Ancestral relation is equal to the transitive closure + of .Indeed, is transitive (see 98 above), contains (indeed, if aRb then, of course, b has every R-hereditary property that all objects x such that aRx have, because b is one of them), and finally, is contained in + (indeed, assume ; take the property to be +; then the two premises, () and (), are obviously satisfied; therefore ...
Family of origin refers to the early social group a person belongs to in childhood, which is often a person's biological family or an adoptive family. [1] The family of origin is often referred to in contrast to the family of choice independently in adulthood (such as marriage , living independently, etc).
The family of choice may or may not include some or all of the members of the family of origin. This family is not one that follows the "normal" familial structure like having a father, a mother, and children. This is family as a group of people that rely on each other like a family of origin would. [42]
Category theory may be viewed as an extension of universal algebra, as the latter studies algebraic structures, and the former applies to any kind of mathematical structure and studies also the relationships between structures of different nature. For this reason, it is used throughout mathematics.
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In linear algebra, a linear relation, or simply relation, between elements of a vector space or a module is a linear equation that has these elements as a solution.. More precisely, if , …, are elements of a (left) module M over a ring R (the case of a vector space over a field is a special case), a relation between , …, is a sequence (, …,) of elements of R such that