σ-algebra

σ-algebra teriminin İngilizce İngilizce sözlükte anlamı: A collection of subsets of a given set, such that the empty set is part of this collection, the collection is closed under complements (with respect to the given set) and the collection is closed under countable unions
Boolean algebra: An algebra with two binary operators which are both associative, both commutative, such that both operators are distributive with respect to each other, with a pair of identity elements: one for each operator, and a unary complementation operator which simultaneously yields the inverse with respect to both operators
The set of divisors of 30, with binary operators: g.c.d. and l.c.m., unary operator: division into 30, and identity elements: 1 and 30, forms a Boolean algebra.
Boolean algebra: An algebra in which all elements can take only one of two values (typically 0 and 1, or "true" and "false") and are subject to operations based on AND, OR and NOT
Borel σ-algebra: The smallest σ-algebra which contains the topology of a given topological space
Lie algebra: A vector space with a specific kind of binary operation on it
abstract algebra: The branch of mathematics concerned with algebraic structures, such as groups, rings, and fields
algebra: A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols
algebra: The study of algebraic structures
algebra: A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences)
algebra: An algebraic structure consisting of a module of a commutative ring along with an additional binary operation that is bilinear
algebra: One of several other types of mathematical structure
algebra: A universal algebra
alternative algebra: An algebra such that every subalgebra generated by two elements is associative
linear algebra: An algebra over a field
linear algebra: The branch of mathematics that deals with vectors, vector spaces, linear transformations and systems of linear equations
modern algebra: The branch of mathematics that deals with groups, monoids, fields, and like algebraic structures
power-associative algebra: An algebra such that every subalgebra generated by one element is associative
universal algebra: A branch of mathematics dealing with equational classes of algebras, where similar theorems from disparate branches of algebra are unified
universal algebra: An algebraic structure studied therein
vector algebra: The branch of mathematics that deals with vectors and operations on them
W algebra: A *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator
W*-algebra: A *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator
von Neumann algebra: A *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator
algebra: {n} literal and universal arithmetic
abstract algebra: Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. Most authors nowadays simply write algebra instead of abstract algebra
Algebra: Algebra is a continuation and extension of the rules of arithmetic into a more general level
Algebra: the mathematics of generalized arithmetical operations
Algebra: A part of mathematics in which signs and letters represent numbers
Algebra: area of math dealing in representing numbers with letters Example: x+5=8 solve for x
Algebra: The study of numbers in general In fact, numbers may not even come into the calculations because they are represented by letters The term comes from the title of an Arabic book - Al-jabr w'al-muqabala - written by Al-Khwarizmi (who lived around the year 800) which is all about algebra
Algebra: is the Arabic al gebr (the equalisation), "the supplementing and equalising (process);" so called because the problems are solved by equations, and the equations are made by supplementary terms Fancifully identified with the Arabian chemist Gebir
Algebra: Algebra is the most basic branch of mathematics It explains the laws that govern the other branches Branches include arithmetic, geometry, trigonometry, and calculus Simple algebra is concerned with the "laws" of arithmetic For example, we can multiply two numbers either way and get the same answer Source: Children's Encyclopedia Britannica vol 1, p 159, 1989
Algebra: The part of mathematics that deals with generalised arithmetic Letters are used to denote variables and unknown numbers and to state general properties
Algebra: Algebra is a major theme in my research For further details, click here
Algebra: The use of variables and the valid manipulation of expressions in the study of numbers
Algebra: ("bind together): a branch of mathematics which describes basic arithmetic relations using variables (letters) The terms are the "words" of an algebraic expression or equation
Algebra: using letters in place of numbers, often if the number is unknown
Boolean algebra: An algebra in which elements have one of two values and the algebraic operations defined on the set are logical OR, a type of addition, and logical AND, a type of multiplication. Symbolic system used for designing logic circuits and networks for digital computers. Its chief utility is in representing the truth value of statements, rather than the numeric quantities handled by ordinary algebra. It lends itself to use in the binary system employed by digital computers, since the only possible truth values, true and false, can be represented by the binary digits 1 and
Boolean algebra: A circuit in computer memory can be open or closed, depending on the value assigned to it, and it is the integrated work of such circuits that give computers their computing ability. The fundamental operations of Boolean logic, often called Boolean operators, are "and," "or," and "not"; combinations of these make up 13 other Boolean operators
algebra: Algebra is a type of mathematics in which letters are used to represent possible quantities. a type of mathematics that uses letters and other signs to represent numbers and values (al-jabr ). algebra and algebraic structures Boolean algebra fundamental theorem of algebra linear algebra
algebra: A structure consisting of a set of elements together with one or more operations and rules specifying what expressions are equivalent
algebra: It is applicable to those relations that are true of every kind of magnitude
algebra: That branch of mathematics which treats of the relations and properties of quantity by means of letters and other symbols
algebra: A treatise on this science
algebra: The study of algebras
algebra: {i} mathematical system that uses equations containing letters and numbers
algebra and algebraic structures: Generalized version of arithmetic that uses variables to stand for unspecified numbers. Its purpose is to solve algebraic equations or systems of equations. Examples of such solutions are the quadratic formula (for solving a quadratic equation) and Gauss-Jordan elimination (for solving a system of equations in matrix form). In higher mathematics, an "algebra" is a structure consisting of a class of objects and a set of rules (analogous to addition and multiplication) for combining them. Basic and higher algebraic structures share two essential characteristics: (1) calculations involve a finite number of steps and (2) calculations involve abstract symbols (usually letters) representing more general objects (usually numbers). Higher algebra (also known as modern or abstract algebra) includes all of elementary algebra, as well as group theory, theory of rings, field theory, manifolds, and vector spaces
boolean algebra: mathematical set with operations whose rules are any of various equivalent systems of postulates
fundamental theorem of algebra: Theorem of equations proved by Carl Friedrich Gauss in 1799. It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers
linear algebra: branch of algebra (Mathematics)
linear algebra: the part of algebra that deals with the theory of linear equations and linear transformation
linear algebra: Branch of algebra concerned with methods of solving systems of linear equations; more generally, the mathematics of linear transformations and vector spaces. "Linear" refers to the form of the equations involved in two dimensions, ax + by = c. Geometrically, this represents a line. If the variables are replaced by vectors, functions, or derivatives, the equation becomes a linear transformation. A system of equations of this type is a system of linear transformations. Because it shows when such a system has a solution and how to find it, linear algebra is essential to the theory of mathematical analysis and differential equations. Its applications extend beyond the physical sciences into, for example, biology and economics
matrix algebra: the part of algebra that deals with the theory of matrices
vector algebra: the part of algebra that deals with the theory of vectors and vector spaces

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