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This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
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 ...
Hug – Form of endearment; Infatuation – Intense but shallow attraction; List of emotions – Contrast of one emotion from another; Social connection – Term in psychology referring to the experience of feeling close and connected to others
The group can be a language or kinship group, a social institution or organization, an economic class, a nation, or gender. Social relations are derived from human behavioral ecology, [2] [3] and, as an aggregate, form a coherent social structure whose constituent parts are best understood relative to each other and to the social ecosystem as a ...
Committed relationship – interpersonal relationship based upon a mutually agreed-upon commitment to one another involving exclusivity, honesty, trust or some other agreed-upon behavior. The term is most commonly used with informal relationships, such as "going steady", but may encompass any relationship where an expressed commitment is involved.
The addition of the is-a-subclass-of relationships creates a taxonomy; a tree-like structure (or, more generally, a partially ordered set) that clearly depicts how objects relate to one another. In such a structure, each object is the 'child' of a 'parent class' (Some languages restrict the is-a-subclass-of relationship to one parent for all ...
Every space treated in Section "Types of spaces" above, except for "Non-commutative geometry", "Schemes" and "Topoi" subsections, is a set (the "principal base set" of the structure, according to Bourbaki) endowed with some additional structure; elements of the base set are usually called "points" of this space. In contrast, elements of (the ...
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".