Table of Contents
91 relations: Addition, Additive inverse, AM–GM inequality, Antisymmetric relation, Approximation, Arithmetic mean, Azuma's inequality, Bell's theorem, Bernoulli's inequality, Binary relation, Boole's inequality, Bracket (mathematics), C (programming language), Cauchy–Schwarz inequality, Chebyshev's inequality, Chernoff bound, Complex number, Converse relation, Cramér–Rao bound, Cylindrical algebraic decomposition, Dense order, Division (mathematics), Domain of a function, Dot product, Double exponential function, Ed Pegg Jr., Elsevier, Euclidean space, Fence (mathematics), Field (mathematics), Fourier–Motzkin elimination, Function (mathematics), Geometric mean, Harmonic mean, Hölder's inequality, Hoeffding's inequality, Inequation, Infimum and supremum, Inner product space, Interval (mathematics), Jensen's inequality, John Wallis, Kolmogorov's inequality, Law of trichotomy, Least-upper-bound property, Lexicographic order, Linear inequality, List of inequalities, List of mathematics competitions, List of triangle inequalities, ... Expand index (41 more) »
Addition
Addition (usually signified by the plus symbol) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.
See Inequality (mathematics) and Addition
Additive inverse
In mathematics, the additive inverse of a number (sometimes called the opposite of) is the number that, when added to, yields zero. Inequality (mathematics) and additive inverse are elementary algebra.
See Inequality (mathematics) and Additive inverse
AM–GM inequality
In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same (in which case they are both that number). Inequality (mathematics) and AM–GM inequality are inequalities.
See Inequality (mathematics) and AM–GM inequality
Antisymmetric relation
In mathematics, a binary relation R on a set X is antisymmetric if there is no pair of distinct elements of X each of which is related by R to the other.
See Inequality (mathematics) and Antisymmetric relation
Approximation
An approximation is anything that is intentionally similar but not exactly equal to something else.
See Inequality (mathematics) and Approximation
Arithmetic mean
In mathematics and statistics, the arithmetic mean, arithmetic average, or just the mean or average (when the context is clear) is the sum of a collection of numbers divided by the count of numbers in the collection.
See Inequality (mathematics) and Arithmetic mean
Azuma's inequality
In probability theory, the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences.
See Inequality (mathematics) and Azuma's inequality
Bell's theorem
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement. Inequality (mathematics) and Bell's theorem are inequalities.
See Inequality (mathematics) and Bell's theorem
Bernoulli's inequality
In mathematics, Bernoulli's inequality (named after Jacob Bernoulli) is an inequality that approximates exponentiations of 1+x. Inequality (mathematics) and Bernoulli's inequality are inequalities.
See Inequality (mathematics) and Bernoulli's inequality
Binary relation
In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain.
See Inequality (mathematics) and Binary relation
Boole's inequality
In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events.
See Inequality (mathematics) and Boole's inequality
Bracket (mathematics)
In mathematics, brackets of various typographical forms, such as parentheses, square brackets, braces and angle brackets ⟨ ⟩, are frequently used in mathematical notation.
See Inequality (mathematics) and Bracket (mathematics)
C (programming language)
C (pronounced – like the letter c) is a general-purpose programming language.
See Inequality (mathematics) and C (programming language)
Cauchy–Schwarz inequality
The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the inner product between two vectors in an inner product space in terms of the product of the vector norms. Inequality (mathematics) and Cauchy–Schwarz inequality are inequalities.
See Inequality (mathematics) and Cauchy–Schwarz inequality
Chebyshev's inequality
In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) provides an upper bound on the probability of deviation of a random variable (with finite variance) from its mean.
See Inequality (mathematics) and Chebyshev's inequality
Chernoff bound
In probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function.
See Inequality (mathematics) and Chernoff bound
Complex number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted, called the imaginary unit and satisfying the equation i^.
See Inequality (mathematics) and Complex number
Converse relation
In mathematics, the converse of a binary relation is the relation that occurs when the order of the elements is switched in the relation.
See Inequality (mathematics) and Converse relation
Cramér–Rao bound
In estimation theory and statistics, the Cramér–Rao bound (CRB) relates to estimation of a deterministic (fixed, though unknown) parameter.
See Inequality (mathematics) and Cramér–Rao bound
Cylindrical algebraic decomposition
In mathematics, cylindrical algebraic decomposition (CAD) is a notion, along with an algorithm to compute it, that is fundamental for computer algebra and real algebraic geometry.
See Inequality (mathematics) and Cylindrical algebraic decomposition
Dense order
In mathematics, a partial order or total order X is said to be dense if, for all x and y in X for which x, there is a z in X such that x. That is, for any two elements, one less than the other, there is another element between them.
See Inequality (mathematics) and Dense order
Division (mathematics)
Division is one of the four basic operations of arithmetic.
See Inequality (mathematics) and Division (mathematics)
Domain of a function
In mathematics, the domain of a function is the set of inputs accepted by the function.
See Inequality (mathematics) and Domain of a function
Dot product
In mathematics, the dot product or scalar productThe term scalar product means literally "product with a scalar as a result".
See Inequality (mathematics) and Dot product
Double exponential function
A double exponential function is a constant raised to the power of an exponential function.
See Inequality (mathematics) and Double exponential function
Ed Pegg Jr.
Edward Taylor Pegg Jr. (born December 7, 1963) is an expert on mathematical puzzles and is a self-described recreational mathematician.
See Inequality (mathematics) and Ed Pegg Jr.
Elsevier
Elsevier is a Dutch academic publishing company specializing in scientific, technical, and medical content.
See Inequality (mathematics) and Elsevier
Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space.
See Inequality (mathematics) and Euclidean space
Fence (mathematics)
In mathematics, a fence, also called a zigzag poset, is a partially ordered set (poset) in which the order relations form a path with alternating orientations: or A fence may be finite, or it may be formed by an infinite alternating sequence extending in both directions.
See Inequality (mathematics) and Fence (mathematics)
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers.
See Inequality (mathematics) and Field (mathematics)
Fourier–Motzkin elimination
Fourier–Motzkin elimination, also known as the FME method, is a mathematical algorithm for eliminating variables from a system of linear inequalities.
See Inequality (mathematics) and Fourier–Motzkin elimination
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of.
See Inequality (mathematics) and Function (mathematics)
Geometric mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite set of real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).
See Inequality (mathematics) and Geometric mean
Harmonic mean
In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means.
See Inequality (mathematics) and Harmonic mean
Hölder's inequality
In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of ''Lp'' spaces. Inequality (mathematics) and Hölder's inequality are inequalities.
See Inequality (mathematics) and Hölder's inequality
Hoeffding's inequality
In probability theory, Hoeffding's inequality provides an upper bound on the probability that the sum of bounded independent random variables deviates from its expected value by more than a certain amount.
See Inequality (mathematics) and Hoeffding's inequality
Inequation
In mathematics, an inequation is a statement that an inequality holds between two values. Inequality (mathematics) and inequation are elementary algebra and mathematical terminology.
See Inequality (mathematics) and Inequation
Infimum and supremum
In mathematics, the infimum (abbreviated inf;: infima) of a subset S of a partially ordered set P is the greatest element in P that is less than or equal to each element of S, if such an element exists.
See Inequality (mathematics) and Infimum and supremum
Inner product space
In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product.
See Inequality (mathematics) and Inner product space
Interval (mathematics)
In mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps".
See Inequality (mathematics) and Interval (mathematics)
Jensen's inequality
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. Inequality (mathematics) and Jensen's inequality are inequalities.
See Inequality (mathematics) and Jensen's inequality
John Wallis
John Wallis (Wallisius) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus.
See Inequality (mathematics) and John Wallis
Kolmogorov's inequality
In probability theory, Kolmogorov's inequality is a so-called "maximal inequality" that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound.
See Inequality (mathematics) and Kolmogorov's inequality
Law of trichotomy
In mathematics, the law of trichotomy states that every real number is either positive, negative, or zero.
See Inequality (mathematics) and Law of trichotomy
Least-upper-bound property
In mathematics, the least-upper-bound property (sometimes called completeness, supremum property or l.u.b. property) is a fundamental property of the real numbers.
See Inequality (mathematics) and Least-upper-bound property
Lexicographic order
In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set.
See Inequality (mathematics) and Lexicographic order
Linear inequality
In mathematics a linear inequality is an inequality which involves a linear function.
See Inequality (mathematics) and Linear inequality
List of inequalities
This article lists Wikipedia articles about named mathematical inequalities. Inequality (mathematics) and list of inequalities are inequalities.
See Inequality (mathematics) and List of inequalities
List of mathematics competitions
Mathematics competitions or mathematical olympiads are competitive events where participants complete a math test.
See Inequality (mathematics) and List of mathematics competitions
List of triangle inequalities
In geometry, triangle inequalities are inequalities involving the parameters of triangles, that hold for every triangle, or for every triangle meeting certain conditions.
See Inequality (mathematics) and List of triangle inequalities
Logical conjunction
In logic, mathematics and linguistics, and (\wedge) is the truth-functional operator of conjunction or logical conjunction.
See Inequality (mathematics) and Logical conjunction
Logical equivalence
In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model.
See Inequality (mathematics) and Logical equivalence
Markov's inequality
In probability theory, Markov's inequality gives an upper bound on the probability that a non-negative random variable is greater than or equal to some positive constant.
See Inequality (mathematics) and Markov's inequality
Material conditional
The material conditional (also known as material implication) is an operation commonly used in logic.
See Inequality (mathematics) and Material conditional
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
See Inequality (mathematics) and Mathematician
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
See Inequality (mathematics) and Mathematics
Minkowski inequality
In mathematical analysis, the Minkowski inequality establishes that the L''p'' spaces are normed vector spaces. Inequality (mathematics) and Minkowski inequality are inequalities.
See Inequality (mathematics) and Minkowski inequality
Monotonic function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
See Inequality (mathematics) and Monotonic function
Multiplication
Multiplication (often denoted by the cross symbol, by the mid-line dot operator, by juxtaposition, or, on computers, by an asterisk) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division.
See Inequality (mathematics) and Multiplication
Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. Inequality (mathematics) and multiplicative inverse are elementary algebra.
See Inequality (mathematics) and Multiplicative inverse
Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to.
See Inequality (mathematics) and Natural logarithm
Negative number
In mathematics, a negative number represents an opposite.
See Inequality (mathematics) and Negative number
Nesbitt's inequality
In mathematics, Nesbitt's inequality, named after Alfred Nesbitt, states that for positive real numbers a, b and c, with equality only when a. Inequality (mathematics) and Nesbitt's inequality are inequalities.
See Inequality (mathematics) and Nesbitt's inequality
Number line
In elementary mathematics, a number line is a picture of a straight line that serves as spatial representation of numbers, usually graduated like a ruler with a particular origin point representing the number zero and evenly spaced marks in either direction representing integers, imagined to extend infinitely.
See Inequality (mathematics) and Number line
Order of magnitude
An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one.
See Inequality (mathematics) and Order of magnitude
Ordered field
In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations.
See Inequality (mathematics) and Ordered field
Partially ordered group
In abstract algebra, a partially ordered group is a group (G, +) equipped with a partial order "≤" that is translation-invariant; in other words, "≤" has the property that, for all a, b, and g in G, if a ≤ b then a + g ≤ b + g and g + a ≤ g + b. An element x of G is called positive if 0 ≤ x.
See Inequality (mathematics) and Partially ordered group
Partially ordered set
In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other.
See Inequality (mathematics) and Partially ordered set
Pedoe's inequality
In geometry, Pedoe's inequality (also Neuberg–Pedoe inequality), named after Daniel Pedoe (1910–1998) and Joseph Jean Baptiste Neuberg (1840–1926), states that if a, b, and c are the lengths of the sides of a triangle with area ƒ, and A, B, and C are the lengths of the sides of a triangle with area F, then with equality if and only if the two triangles are similar with pairs of corresponding sides (A, a), (B, b), and (C, c).
See Inequality (mathematics) and Pedoe's inequality
Pierre Bouguer
Pierre Bouguer (16 February 1698, Le Croisic – 15 August 1758, Paris) was a French mathematician, geophysicist, geodesist, and astronomer.
See Inequality (mathematics) and Pierre Bouguer
Poincaré inequality
In mathematics, the Poincaré inequality is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. Inequality (mathematics) and Poincaré inequality are inequalities.
See Inequality (mathematics) and Poincaré inequality
Programming language
A programming language is a system of notation for writing computer programs.
See Inequality (mathematics) and Programming language
Property (philosophy)
In logic and philosophy (especially metaphysics), a property is a characteristic of an object; a red object is said to have the property of redness.
See Inequality (mathematics) and Property (philosophy)
Python (programming language)
Python is a high-level, general-purpose programming language.
See Inequality (mathematics) and Python (programming language)
Real number
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
See Inequality (mathematics) and Real number
Reflexive relation
In mathematics, a binary relation R on a set X is reflexive if it relates every element of X to itself.
See Inequality (mathematics) and Reflexive relation
Relational operator
In computer science, a relational operator is a programming language construct or operator that tests or defines some kind of relation between two entities.
See Inequality (mathematics) and Relational operator
Root mean square
In mathematics, the root mean square (abbrev. RMS, or rms) of a set of numbers is the square root of the set's mean square.
See Inequality (mathematics) and Root mean square
Row and column vectors
In linear algebra, a column vector with elements is an m \times 1 matrix consisting of a single column of entries, for example, \boldsymbol.
See Inequality (mathematics) and Row and column vectors
Samuelson's inequality
In statistics, Samuelson's inequality, named after the economist Paul Samuelson, also called the Laguerre–Samuelson inequality, after the mathematician Edmond Laguerre, states that every one of any collection x1,..., xn, is within uncorrected sample standard deviations of their sample mean.
See Inequality (mathematics) and Samuelson's inequality
Set (mathematics)
In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
See Inequality (mathematics) and Set (mathematics)
Sign (mathematics)
In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Inequality (mathematics) and sign (mathematics) are mathematical terminology.
See Inequality (mathematics) and Sign (mathematics)
Sobolev inequality
In mathematics, there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. Inequality (mathematics) and Sobolev inequality are inequalities.
See Inequality (mathematics) and Sobolev inequality
Subset
In mathematics, a 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).
See Inequality (mathematics) and Subset
Subtraction
Subtraction (which is signified by the minus sign) is one of the four arithmetic operations along with addition, multiplication and division.
See Inequality (mathematics) and Subtraction
Total order
In mathematics, a total order or linear order is a partial order in which any two elements are comparable.
See Inequality (mathematics) and Total order
Transitive relation
In mathematics, a binary relation on a set is transitive if, for all elements,, in, whenever relates to and to, then also relates to. Inequality (mathematics) and transitive relation are elementary algebra.
See Inequality (mathematics) and Transitive relation
Triangle inequality
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
See Inequality (mathematics) and Triangle inequality
Ultrarelativistic limit
In physics, a particle is called ultrarelativistic when its speed is very close to the speed of light.
See Inequality (mathematics) and Ultrarelativistic limit
Universal quantification
In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", or "for any".
See Inequality (mathematics) and Universal quantification
Upper and lower bounds
In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is every element of. Inequality (mathematics) and upper and lower bounds are mathematical terminology.
See Inequality (mathematics) and Upper and lower bounds
References
Also known as Algebraic inequality, Comparison (mathematics), Complex number inequality, Equal or greater than, Equal or greater than sign, Equal or greater-than, Equal or greater-than sign, Equal or less than, Equal or less than sign, Equal or less-than, Equal or less-than sign, Greater or equal sign, Greater or equal to, Greater than, Greater than or equal, Greater than or equal to, Greater-than, Inequal, Inequalities between complex numbers, Inequalities of complex numbers, Inequality (math), Inequality bracket, Inequality brackets, Inequality notation, Inequality sign, Inequality signs, Inequality symbol, Inequality symbols, Inequalty, Less Than, Less or equal, Less or equal than, Less than or equal, Less than or equal to, Less than or equals, Less-than, Lesser than, Lessthan, Much greater than, Much less than, Much-greater-than sign, Much-less-than sign, Power inequalities, Quadratic inequality, Sharp inequalities, Smaller than, Strict inequality, System of inequalities, System of polynomial inequalities, Systems of polynomial inequalities, Transitive property of inequality, Vector inequalities, .