Algebra of setsIn mathematics, the algebra of sets, not to be confused with the mathematical structure of an algebra of sets, defines the properties and laws of sets, 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.
Field of setsIn mathematics, a field of sets is a mathematical structure consisting of a pair consisting of a set and a family of subsets of called an algebra over that contains the empty set as an element, and is closed under the operations of taking complements in finite unions, and finite intersections. Fields of sets should not be confused with fields in ring theory nor with fields in physics. Similarly the term "algebra over " is used in the sense of a Boolean algebra and should not be confused with algebras over fields or rings in ring theory.
Product (mathematics)In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors. For example, 21 is the product of 3 and 7 (the result of multiplication), and is the product of and (indicating that the two factors should be multiplied together). When one factor is an integer, the product is called a multiple. The order in which real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of multiplication.
Set theorySet theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.
Index setIn mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set A may be indexed or labeled by means of the elements of a set J, then J is an index set. The indexing consists of a surjective function from J onto A, and the indexed collection is typically called an indexed family, often written as {Aj}j∈J. An enumeration of a set S gives an index set , where f : J → S is the particular enumeration of S.
Queer studiesQueer studies, sexual diversity studies, or LGBT studies is the study of topics relating to sexual orientation and gender identity usually focusing on lesbian, gay, bisexual, transgender, gender dysphoria, asexual, queer, questioning, intersex people and cultures. Originally centered on LGBT history and literary theory, the field has expanded to include the academic study of issues raised in archaeology, sociology, psychiatry, anthropology, the history of science, philosophy, psychology, sexology, political science, ethics, and other fields by an examination of the identity, lives, history, and perception of being queer.
Klinefelter syndromeKlinefelter syndrome (KS), also known as 47,XXY, is an aneuploid genetic condition where a male has an additional copy of the X chromosome. The primary features are infertility and small, poorly functioning testicles. Usually, symptoms are subtle and subjects do not realize they are affected. Sometimes, symptoms are more evident and may include weaker muscles, greater height, poor motor coordination, less body hair, breast growth, and less interest in sex. Often, these symptoms are noticed only at puberty.
Women's studiesWomen's studies is an academic field that draws on feminist and interdisciplinary methods to place women's lives and experiences at the center of study, while examining social and cultural constructs of gender; systems of privilege and oppression; and the relationships between power and gender as they intersect with other identities and social locations such as race, sexual orientation, socio-economic class, and disability.
XYY syndromeXYY syndrome, also known as Jacobs syndrome, is an aneuploid genetic condition in which a male has an extra Y chromosome. There are usually few symptoms. These may include being taller than average and an increased risk of learning disabilities. The person is generally otherwise normal, including typical rates of fertility. The condition is generally not inherited but rather occurs as a result of a random event during sperm development. Diagnosis is by a chromosomal analysis, but most of those affected are not diagnosed within their lifetime.
SubsetIn mathematics, set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements. The subset relation defines a partial order on sets.
Parental leaveParental leave, or family leave, is an employee benefit available in almost all countries. The term "parental leave" may include maternity, paternity, and adoption leave; or may be used distinctively from "maternity leave" and "paternity leave" to describe separate family leave available to either parent to care for small children. In some countries and jurisdictions, "family leave" also includes leave provided to care for ill family members. Often, the minimum benefits and eligibility requirements are stipulated by law.
Empty setIn mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called non-empty. In some textbooks and popularizations, the empty set is referred to as the "null set".
