Table of Contents
172 relations: Abstract nonsense, Aleph number, Alexander Grothendieck, Algebra over a field, Algebraic geometry, Algebraic number, Algebraic variety, Algebraically closed field, Almost all, Analytic function, Angle, Antichain, Arbitrarily large, Arbitrariness, Arithmetic, Back-of-the-envelope calculation, Basis (linear algebra), Binary relation, Canonical form, Canonical map, Cardinality, Category (mathematics), Category theory, Commutative diagram, Compact space, Complement (set theory), Complex analysis, Continuous function, Corollary, Countable set, Cover (topology), Dense set, Derivative, Differentiable function, Differential operator, Dimension (vector space), Dirichlet function, Divisor, Donaldson's theorem, E (mathematical constant), Element (category theory), Elementary proof, Encyclopedia of Mathematics, Equation, Equivalence class, Equivalence relation, Euclid's theorem, Euler's theorem, Eventually (mathematics), Exact category, ... Expand index (122 more) »
- Glossaries of mathematics
Abstract nonsense
In mathematics, abstract nonsense, general abstract nonsense, generalized abstract nonsense, and general nonsense are nonderogatory terms used by mathematicians to describe long, theoretical parts of a proof they skip over when readers are expected to be familiar with them. Glossary of mathematical jargon and abstract nonsense are mathematical terminology.
See Glossary of mathematical jargon and Abstract nonsense
Aleph number
In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets that can be well-ordered.
See Glossary of mathematical jargon and Aleph number
Alexander Grothendieck
Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born mathematician who became the leading figure in the creation of modern algebraic geometry.
See Glossary of mathematical jargon and Alexander Grothendieck
Algebra over a field
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.
See Glossary of mathematical jargon and Algebra over a field
Algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.
See Glossary of mathematical jargon and Algebraic geometry
Algebraic number
An algebraic number is a number that is a root of a non-zero polynomial (of finite degree) in one variable with integer (or, equivalently, rational) coefficients.
See Glossary of mathematical jargon and Algebraic number
Algebraic variety
Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics.
See Glossary of mathematical jargon and Algebraic variety
Algebraically closed field
In mathematics, a field is algebraically closed if every non-constant polynomial in (the univariate polynomial ring with coefficients in) has a root in.
See Glossary of mathematical jargon and Algebraically closed field
Almost all
In mathematics, the term "almost all" means "all but a negligible quantity". Glossary of mathematical jargon and Almost all are mathematical terminology.
See Glossary of mathematical jargon and Almost all
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
See Glossary of mathematical jargon and Analytic function
Angle
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
See Glossary of mathematical jargon and Angle
Antichain
In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two distinct elements in the subset are incomparable.
See Glossary of mathematical jargon and Antichain
Arbitrarily large
In mathematics, the phrases arbitrarily large, arbitrarily small and arbitrarily long are used in statements to make clear the fact that an object is large, small, or long with little limitation or restraint, respectively. Glossary of mathematical jargon and arbitrarily large are mathematical terminology.
See Glossary of mathematical jargon and Arbitrarily large
Arbitrariness
Arbitrariness is the quality of being "determined by chance, whim, or impulse, and not by necessity, reason, or principle".
See Glossary of mathematical jargon and Arbitrariness
Arithmetic
Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division.
See Glossary of mathematical jargon and Arithmetic
Back-of-the-envelope calculation
A back-of-the-envelope calculation is a rough calculation, typically jotted down on any available scrap of paper such as an envelope.
See Glossary of mathematical jargon and Back-of-the-envelope calculation
Basis (linear algebra)
In mathematics, a set of vectors in a vector space is called a basis (bases) if every element of may be written in a unique way as a finite linear combination of elements of.
See Glossary of mathematical jargon and Basis (linear algebra)
Binary relation
In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain.
See Glossary of mathematical jargon and Binary relation
Canonical form
In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Glossary of mathematical jargon and canonical form are mathematical terminology.
See Glossary of mathematical jargon and Canonical form
Canonical map
In mathematics, a canonical map, also called a natural map, is a map or morphism between objects that arises naturally from the definition or the construction of the objects. Glossary of mathematical jargon and canonical map are mathematical terminology.
See Glossary of mathematical jargon and Canonical map
Cardinality
In mathematics, the cardinality of a set is a measure of the number of elements of the set.
See Glossary of mathematical jargon and Cardinality
Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked by "arrows".
See Glossary of mathematical jargon and Category (mathematics)
Category theory
Category theory is a general theory of mathematical structures and their relations.
See Glossary of mathematical jargon and Category theory
Commutative diagram
The commutative diagram used in the proof of the five lemma In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. Glossary of mathematical jargon and commutative diagram are mathematical terminology.
See Glossary of mathematical jargon and Commutative diagram
Compact space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space.
See Glossary of mathematical jargon and Compact space
Complement (set theory)
In set theory, the complement of a set, often denoted by A^\complement, is the set of elements not in.
See Glossary of mathematical jargon and Complement (set theory)
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
See Glossary of mathematical jargon and Complex analysis
Continuous function
In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function.
See Glossary of mathematical jargon and Continuous function
Corollary
In mathematics and logic, a corollary is a theorem of less importance which can be readily deduced from a previous, more notable statement. Glossary of mathematical jargon and corollary are mathematical terminology.
See Glossary of mathematical jargon and Corollary
Countable set
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers.
See Glossary of mathematical jargon and Countable set
Cover (topology)
In mathematics, and more particularly in set theory, a cover (or covering) of a set X is a family of subsets of X whose union is all of X. More formally, if C.
See Glossary of mathematical jargon and Cover (topology)
Dense set
In topology and related areas of mathematics, a subset A of a topological space X is said to be dense in X if every point of X either belongs to A or else is arbitrarily "close" to a member of A — for instance, the rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).
See Glossary of mathematical jargon and Dense set
Derivative
The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function's output with respect to its input.
See Glossary of mathematical jargon and Derivative
Differentiable function
In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
See Glossary of mathematical jargon and Differentiable function
Differential operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator.
See Glossary of mathematical jargon and Differential operator
Dimension (vector space)
In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field.
See Glossary of mathematical jargon and Dimension (vector space)
Dirichlet function
In mathematics, the Dirichlet function is the indicator function \mathbf_\Q of the set of rational numbers \Q, i.e. \mathbf_\Q(x).
See Glossary of mathematical jargon and Dirichlet function
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.
See Glossary of mathematical jargon and Divisor
Donaldson's theorem
In mathematics, and especially differential topology and gauge theory, Donaldson's theorem states that a definite intersection form of a compact, oriented, smooth manifold of dimension 4 is diagonalisable.
See Glossary of mathematical jargon and Donaldson's theorem
E (mathematical constant)
The number is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways.
See Glossary of mathematical jargon and E (mathematical constant)
Element (category theory)
In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any category.
See Glossary of mathematical jargon and Element (category theory)
Elementary proof
In mathematics, an elementary proof is a mathematical proof that only uses basic techniques.
See Glossary of mathematical jargon and Elementary proof
Encyclopedia of Mathematics
The Encyclopedia of Mathematics (also EOM and formerly Encyclopaedia of Mathematics) is a large reference work in mathematics.
See Glossary of mathematical jargon and Encyclopedia of Mathematics
Equation
In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign.
See Glossary of mathematical jargon and Equation
Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set S into equivalence classes.
See Glossary of mathematical jargon and Equivalence class
Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
See Glossary of mathematical jargon and Equivalence relation
Euclid's theorem
Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers.
See Glossary of mathematical jargon and Euclid's theorem
Euler's theorem
In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if and are coprime positive integers, then a^ is congruent to 1 modulo, where \varphi denotes Euler's totient function; that is In 1736, Leonhard Euler published a proof of Fermat's little theorem (stated by Fermat without proof), which is the restriction of Euler's theorem to the case where is a prime number.
See Glossary of mathematical jargon and Euler's theorem
Eventually (mathematics)
In the mathematical areas of number theory and analysis, an infinite sequence or a function is said to eventually have a certain property, if it does not have the said property across all its ordered instances, but will after some instances have passed. Glossary of mathematical jargon and eventually (mathematics) are mathematical terminology.
See Glossary of mathematical jargon and Eventually (mathematics)
Exact category
In mathematics, specifically in category theory, an exact category is a category equipped with short exact sequences.
See Glossary of mathematical jargon and Exact category
Exponential function
The exponential function is a mathematical function denoted by f(x).
See Glossary of mathematical jargon and Exponential function
Extended real number line
In mathematics, the extended real number system is obtained from the real number system \R by adding two infinity elements: +\infty and -\infty, where the infinities are treated as actual numbers.
See Glossary of mathematical jargon and Extended real number line
Fermat's little theorem
In number theory, Fermat's little theorem states that if is a prime number, then for any integer, the number is an integer multiple of.
See Glossary of mathematical jargon and Fermat's little theorem
Fiber bundle
In mathematics, and particularly topology, a fiber bundle (''Commonwealth English'': fibre bundle) is a space that is a product space, but may have a different topological structure.
See Glossary of mathematical jargon and Fiber bundle
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 Glossary of mathematical jargon and Field (mathematics)
Field extension
In mathematics, particularly in algebra, a field extension (denoted L/K) is a pair of fields K \subseteq L, such that the operations of K are those of L restricted to K. In this case, L is an extension field of K and K is a subfield of L. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers.
See Glossary of mathematical jargon and Field extension
Forgetful functor
In mathematics, in the area of category theory, a forgetful functor (also known as a stripping functor) 'forgets' or drops some or all of the input's structure or properties 'before' mapping to the output.
See Glossary of mathematical jargon and Forgetful functor
Formal proof
In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence, according to the rule of inference.
See Glossary of mathematical jargon and Formal proof
Formal system
A formal system is an abstract structure and formalization of an axiomatic system used for inferring theorems from axioms by a set of inference rules.
See Glossary of mathematical jargon and Formal system
Fraction
A fraction (from fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.
See Glossary of mathematical jargon and Fraction
French language
French (français,, or langue française,, or by some speakers) is a Romance language of the Indo-European family.
See Glossary of mathematical jargon and French language
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of.
See Glossary of mathematical jargon and Function (mathematics)
Fundamental theorem of arithmetic
In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors.
See Glossary of mathematical jargon and Fundamental theorem of arithmetic
Generic property
In mathematics, properties that hold for "typical" examples are called generic properties.
See Glossary of mathematical jargon and Generic property
Geometry
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
See Glossary of mathematical jargon and Geometry
Gian-Carlo Rota
Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician and philosopher.
See Glossary of mathematical jargon and Gian-Carlo Rota
Glossary of areas of mathematics
Mathematics is a broad subject that is commonly divided in many areas that may be defined by their objects of study, by the used methods, or by both. Glossary of mathematical jargon and Glossary of areas of mathematics are Glossaries of mathematics.
See Glossary of mathematical jargon and Glossary of areas of mathematics
Glossary of mathematical jargon
The language of mathematics has a vast vocabulary of specialist and technical terms. Glossary of mathematical jargon and Glossary of mathematical jargon are Glossaries of mathematics and mathematical terminology.
See Glossary of mathematical jargon and Glossary of mathematical jargon
Glossary of mathematical symbols
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. Glossary of mathematical jargon and Glossary of mathematical symbols are Glossaries of mathematics.
See Glossary of mathematical jargon and Glossary of mathematical symbols
Hand-waving
Hand-waving (with various spellings) is a pejorative label for attempting to be seen as effective – in word, reasoning, or deed – while actually doing nothing effective or substantial. Glossary of mathematical jargon and Hand-waving are mathematical terminology.
See Glossary of mathematical jargon and Hand-waving
Hölder condition
In mathematics, a real or complex-valued function on -dimensional Euclidean space satisfies a Hölder condition, or is Hölder continuous, when there are real constants,, such that | f(x) - f(y) | \leq C\| x - y\|^ for all and in the domain of.
See Glossary of mathematical jargon and Hölder condition
Heuristic
A heuristic or heuristic technique (problem solving, mental shortcut, rule of thumb) is any approach to problem solving that employs a pragmatic method that is not fully optimized, perfected, or rationalized, but is nevertheless "good enough" as an approximation or attribute substitution.
See Glossary of mathematical jargon and Heuristic
Idempotence
Idempotence is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application.
See Glossary of mathematical jargon and Idempotence
Injective function
In mathematics, an injective function (also known as injection, or one-to-one function) is a function that maps distinct elements of its domain to distinct elements; that is, implies.
See Glossary of mathematical jargon and Injective function
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 Glossary of mathematical jargon and Inner product space
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.
See Glossary of mathematical jargon and Integer
Intersection (set theory)
In set theory, the intersection of two sets A and B, denoted by A \cap B, is the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A.
See Glossary of mathematical jargon and Intersection (set theory)
Interval (mathematics)
In mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps".
See Glossary of mathematical jargon and Interval (mathematics)
Intransitivity
In mathematics, intransitivity (sometimes called nontransitivity) is a property of binary relations that are not transitive relations.
See Glossary of mathematical jargon and Intransitivity
Invariant (mathematics)
In mathematics, an invariant is a property of a mathematical object (or a class of mathematical objects) which remains unchanged after operations or transformations of a certain type are applied to the objects. Glossary of mathematical jargon and invariant (mathematics) are mathematical terminology.
See Glossary of mathematical jargon and Invariant (mathematics)
Irrational number
In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers.
See Glossary of mathematical jargon and Irrational number
Jargon
Jargon or technical language is the specialized terminology associated with a particular field or area of activity.
See Glossary of mathematical jargon and Jargon
Lagrange's theorem (group theory)
In the mathematical field of group theory, Lagrange's theorem is a theorem that states that for any finite group, the order (number of elements) of every subgroup of divides the order of.
See Glossary of mathematical jargon and Lagrange's theorem (group theory)
Language of mathematics
The language of mathematics or mathematical language is an extension of the natural language (for example English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proofs, logical deductions, etc.) with concision, precision and unambiguity.
See Glossary of mathematical jargon and Language of mathematics
Lift (mathematics)
In category theory, a branch of mathematics, given a morphism f: X → Y and a morphism g: Z → Y, a lift or lifting of f to Z is a morphism h: X → Z such that.
See Glossary of mathematical jargon and Lift (mathematics)
Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.
See Glossary of mathematical jargon and Limit (mathematics)
Lindelöf space
In mathematics, a Lindelöf space is a topological space in which every open cover has a countable subcover.
See Glossary of mathematical jargon and Lindelöf space
Linear algebraic group
In mathematics, a linear algebraic group is a subgroup of the group of invertible n\times n matrices (under matrix multiplication) that is defined by polynomial equations.
See Glossary of mathematical jargon and Linear algebraic group
Linear map
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication.
See Glossary of mathematical jargon and Linear map
List of mathematical constants
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems.
See Glossary of mathematical jargon and List of mathematical constants
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 Glossary of mathematical jargon and Logical equivalence
Logical intuition
Logical Intuition, or mathematical intuition or rational intuition, is a series of instinctive foresight, know-how, and savviness often associated with the ability to perceive logical or mathematical truth—and the ability to solve mathematical challenges efficiently.
See Glossary of mathematical jargon and Logical intuition
Mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.
See Glossary of mathematical jargon and Mathematical analysis
Mathematical beauty
Mathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Glossary of mathematical jargon and Mathematical beauty are mathematical terminology.
See Glossary of mathematical jargon and Mathematical beauty
Mathematical diagram
Mathematical diagrams, such as charts and graphs, are mainly designed to convey mathematical relationships—for example, comparisons over time.
See Glossary of mathematical jargon and Mathematical diagram
Mathematical folklore
In common mathematical parlance, a mathematical result is called folklore if it is an unpublished result with no clear originator, but which is well-circulated and believed to be true among the specialists.
See Glossary of mathematical jargon and Mathematical folklore
Mathematical induction
Mathematical induction is a method for proving that a statement P(n) is true for every natural number n, that is, that the infinitely many cases P(0), P(1), P(2), P(3), \dots  all hold.
See Glossary of mathematical jargon and Mathematical induction
Mathematical object
A mathematical object is an abstract concept arising in mathematics.
See Glossary of mathematical jargon and Mathematical object
Mathematical proof
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. Glossary of mathematical jargon and mathematical proof are mathematical terminology.
See Glossary of mathematical jargon and Mathematical proof
Mathematical structure
In mathematics, a structure is a set provided with some additional features on the set (e.g. an operation, relation, metric, or topology).
See Glossary of mathematical jargon and Mathematical structure
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 Glossary of mathematical jargon and Mathematics
Meagre set
In the mathematical field of general topology, a meagre set (also called a meager set or a set of first category) is a subset of a topological space that is small or negligible in a precise sense detailed below.
See Glossary of mathematical jargon and Meagre set
Measure (mathematics)
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events.
See Glossary of mathematical jargon and Measure (mathematics)
Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus.
See Glossary of mathematical jargon and Modular arithmetic
Monoidal category
In mathematics, a monoidal category (or tensor category) is a category \mathbf C equipped with a bifunctor that is associative up to a natural isomorphism, and an object I that is both a left and right identity for ⊗, again up to a natural isomorphism.
See Glossary of mathematical jargon and Monoidal category
Morphism
In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between algebraic structures, functions from a set to another set, and continuous functions between topological spaces.
See Glossary of mathematical jargon and Morphism
Multivalued function
In mathematics, a multivalued function (also known as a multiple-valued function) is a function that has two or more values in its range for at least one point in its domain.
See Glossary of mathematical jargon and Multivalued function
Natural transformation
In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved.
See Glossary of mathematical jargon and Natural transformation
Necessity and sufficiency
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. Glossary of mathematical jargon and necessity and sufficiency are mathematical terminology.
See Glossary of mathematical jargon and Necessity and sufficiency
Negation
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P to another proposition "not P", standing for "P is not true", written \neg P, \mathord P or \overline.
See Glossary of mathematical jargon and Negation
Normal subgroup
In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part.
See Glossary of mathematical jargon and Normal subgroup
Null set
In mathematical analysis, a null set is a Lebesgue measurable set of real numbers that has measure zero.
See Glossary of mathematical jargon and Null set
Number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.
See Glossary of mathematical jargon and Number theory
Open set
In mathematics, an open set is a generalization of an open interval in the real line.
See Glossary of mathematical jargon and Open set
Operator overloading
In computer programming, operator overloading, sometimes termed operator ad hoc polymorphism, is a specific case of polymorphism, where different operators have different implementations depending on their arguments.
See Glossary of mathematical jargon and Operator overloading
Parity (mathematics)
In mathematics, parity is the property of an integer of whether it is even or odd.
See Glossary of mathematical jargon and Parity (mathematics)
Pathological (mathematics)
In mathematics, when a mathematical phenomenon runs counter to some intuition, then the phenomenon is sometimes called pathological. Glossary of mathematical jargon and pathological (mathematics) are mathematical terminology.
See Glossary of mathematical jargon and Pathological (mathematics)
Pi
The number (spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.
See Glossary of mathematical jargon and Pi
Pierre-Simon Laplace
Pierre-Simon, Marquis de Laplace (23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy.
See Glossary of mathematical jargon and Pierre-Simon Laplace
Platonic solid
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space.
See Glossary of mathematical jargon and Platonic solid
Polynomial ring
In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.
See Glossary of mathematical jargon and Polynomial ring
Prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.
See Glossary of mathematical jargon and Prime number
Prime number theorem
In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers.
See Glossary of mathematical jargon and Prime number theorem
Projection (mathematics)
In mathematics, a projection is an idempotent mapping of a set (or other mathematical structure) into a subset (or sub-structure). Glossary of mathematical jargon and projection (mathematics) are mathematical terminology.
See Glossary of mathematical jargon and Projection (mathematics)
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.
See Glossary of mathematical jargon and Projective geometry
Proof by contradiction
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction.
See Glossary of mathematical jargon and Proof by contradiction
Proof by exhaustion
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds.
See Glossary of mathematical jargon and Proof by exhaustion
Proof by intimidation
Proof by intimidation (or argumentum verbosum) is a jocular phrase used mainly in mathematics to refer to a specific form of hand-waving whereby one attempts to advance an argument by giving an argument loaded with jargon and obscure results or by marking it as obvious or trivial.
See Glossary of mathematical jargon and Proof by intimidation
Proper morphism
In algebraic geometry, a proper morphism between schemes is an analog of a proper map between complex analytic spaces.
See Glossary of mathematical jargon and Proper morphism
Q.E.D.
Q.E.D. or QED is an initialism of the Latin phrase quod erat demonstrandum, meaning "that which was to be demonstrated". Glossary of mathematical jargon and Q.E.D. are mathematical terminology.
See Glossary of mathematical jargon and Q.E.D.
Quadratic equation
In mathematics, a quadratic equation is an equation that can be rearranged in standard form as ax^2 + bx + c.
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Quadratic function
In mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables.
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Real analysis
In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions.
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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.
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Reflexive relation
In mathematics, a binary relation R on a set X is reflexive if it relates every element of X to itself.
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Regular graph
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency.
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Regular space
In topology and related fields of mathematics, a topological space X is called a regular space if every closed subset C of X and a point p not contained in C have non-overlapping open neighborhoods.
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Samuel Eilenberg
Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with Saunders Mac Lane) and homological algebra.
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Saunders Mac Lane
Saunders Mac Lane (August 4, 1909 – April 14, 2005), born Leslie Saunders MacLane, was an American mathematician who co-founded category theory with Samuel Eilenberg.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
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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.
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Sides of an equation
In mathematics, LHS is informal shorthand for the left-hand side of an equation. Glossary of mathematical jargon and sides of an equation are mathematical terminology.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number, called differentiability class, of continuous derivatives it has over its domain.
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Square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four sides of equal length and four equal angles (90-degree angles, π/2 radian angles, or right angles).
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Square root of 2
The square root of 2 (approximately 1.4142) is a real number that, when multiplied by itself or squared, equals the number 2.
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Stefan Banach
Stefan Banach (30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the 20th century's most important and influential mathematicians.
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Strong antichain
In order theory, a subset A of a partially ordered set P is a strong downwards antichain if it is an antichain in which no two distinct elements have a common lower bound in P, that is, In the case where P is ordered by inclusion, and closed under subsets, but does not contain the empty set, this is simply a family of pairwise disjoint sets.
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Strongly regular graph
In graph theory, a strongly regular graph (SRG) is a regular graph with vertices and degree such that for some given integers \lambda, \mu \ge 0.
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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).
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Surjective function
In mathematics, a surjective function (also known as surjection, or onto function) is a function such that, for every element of the function's codomain, there exists one element in the function's domain such that.
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TFAE
TFAE may refer to.
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Theorem
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. Glossary of mathematical jargon and theorem are mathematical terminology.
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Tombstone (typography)
In mathematics, the tombstone, halmos, end-of-proof, or Q.E.D. symbol "∎" (or "□") is a symbol used to denote the end of a proof, in place of the traditional abbreviation "Q.E.D." for the Latin phrase "quod erat demonstrandum".
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Tongue-in-cheek
Tongue-in-cheek is an idiom that describes a humorous or sarcastic statement expressed in a serious manner.
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Topological property
In topology and related areas of mathematics, a topological property or topological invariant is a property of a topological space that is invariant under homeomorphisms.
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Topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.
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Transcendental number
In mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients.
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Transformation (function)
In mathematics, a transformation or self-map is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e..
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Transport of structure
In mathematics, particularly in universal algebra and category theory, transport of structure refers to the process whereby a mathematical object acquires a new structure and its canonical definitions, as a result of being isomorphic to (or otherwise identified with) another object with a pre-existing structure. Glossary of mathematical jargon and transport of structure are mathematical terminology.
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Triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry.
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Triviality (mathematics)
In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or an object which possesses a simple structure (e.g., groups, topological spaces). Glossary of mathematical jargon and Triviality (mathematics) are mathematical terminology.
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Uniqueness quantification
In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. Glossary of mathematical jargon and Uniqueness quantification are mathematical terminology.
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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".
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Up to
Two mathematical objects and are called "equal up to an equivalence relation ". Glossary of mathematical jargon and up to are mathematical terminology.
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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. Glossary of mathematical jargon and upper and lower bounds are mathematical terminology.
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Vanish at infinity
In mathematics, a function is said to vanish at infinity if its values approach 0 as the input grows without bounds.
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Variance
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable.
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Vector space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', can be added together and multiplied ("scaled") by numbers called ''scalars''.
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Vocabulary
A vocabulary (also known as a lexicon) is a set of words, typically the set in a language or the set known to an individual.
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Weierstrass function
In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere.
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Without loss of generality
Without loss of generality (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is a frequently used expression in mathematics. Glossary of mathematical jargon and without loss of generality are mathematical terminology.
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Zariski topology
In algebraic geometry and commutative algebra, the Zariski topology is a topology defined on geometric objects called varieties.
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See also
Glossaries of mathematics
- Glossary of Lie groups and Lie algebras
- Glossary of Principia Mathematica
- Glossary of Riemannian and metric geometry
- Glossary of algebraic geometry
- Glossary of algebraic topology
- Glossary of areas of mathematics
- Glossary of arithmetic and diophantine geometry
- Glossary of calculus
- Glossary of category theory
- Glossary of classical algebraic geometry
- Glossary of commutative algebra
- Glossary of cryptographic keys
- Glossary of differential geometry and topology
- Glossary of experimental design
- Glossary of field theory
- Glossary of functional analysis
- Glossary of game theory
- Glossary of general topology
- Glossary of graph theory
- Glossary of group theory
- Glossary of invariant theory
- Glossary of linear algebra
- Glossary of mathematical jargon
- Glossary of mathematical symbols
- Glossary of module theory
- Glossary of number theory
- Glossary of order theory
- Glossary of probability and statistics
- Glossary of real and complex analysis
- Glossary of representation theory
- Glossary of ring theory
- Glossary of set theory
- Glossary of shapes with metaphorical names
- Glossary of symplectic geometry
- Glossary of systems theory
- Glossary of tensor theory
References
Also known as Aliter, Angle chase, Angle chasing, By inspection, Deep result, Factor through, Glossary of mathematics, In general, List of mathematical jargon, Math jargon, Mathematical jargon, Proof by inspection.