n
(mathematical analysis, computing) A model for self-validated numerical analysis in which quantities are represented as affine combinations (called affine forms) of certain primitive variables that stand for sources of uncertainty in data or approximations made during computations.
n
(uncountable, mathematics) A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
adj
(mathematics, of an expression, equation, or function) Containing only numbers, letters, and arithmetic operators.
n
(computing theory) One of the three rewrite rules of lambda calculus, in which a bound variable of a lambda term is replaced by another variable across its entire scope. So if there is a lambda term of the form (𝜆x.t) and it is desired to have x replaced with y, then the rewritten lambda term would have the form (𝜆y.t[y/x]) where t[y/x], "t with y instead of x", has had all free instances of x in t replaced with y.
adj
(set theory, order theory, of a poset X with partial order ≤) That contains a least element, a, and a greatest element, b, such that for all x ∈ X, a ≤ x ≤ b.
n
(mathematics, computing theory) A theorem stating that, when applying reduction rules to terms in the lambda calculus, the ordering in which the reductions are chosen makes no difference to the eventual result.
n
(mathematics) A developing branch of mathematics in which techniques of algebraic geometry are applied to number theory (specifically the theory of Diophantine equations), in particular being concerned with algebraic varieties over fields that are finitely generated over their prime fields and over local fields.
v
(mathematics, transitive) To divide an expression into a list of items that, when multiplied together, will produce the original quantity.
n
(mathematics, number theory) A number equal to the number of dots in a geometric figure formed of dots. The series begins with unity and is formed so that subtracting each from the following, and treating the series so formed in the same way, by a continuation of the process, yields equal differences.
n
(set theory) A diagram which represents a finite poset, in which nodes are elements of the poset and arrows represent the order relation between elements. Transitivity of the order relation is tacit, in other words, if x
n
(probability) A theorem relating the weak convergence of cumulative distribution functions to the convergence of expectations of certain measurable functions.
n
The improved or modified Euler method (that is, the explicit trapezoidal rule).
n
(algebra, order theory) A bounded lattice, L, modified to serve as a model for a logical calculus by being equipped with a binary operation called "implies", denoted → (sometimes ⊃ or ⇒), defined such that (a→b)∧a ≤ b and, moreover, that x = a→b is the greatest element such that x∧a ≤ b (in the sense that if c∧a ≤ b then c ≤ a→b).
n
(arithmetic) A vulgar fraction of which the numerator has a greater magnitude than the denominator, such as 3/2.
n
(mathematics) A method of proof by contradiction that is used to prove that a statement must be false for all positive integers. By showing that if it is true for one integer, it must be true for a smaller integer, an infinite number of solutions are found and a contradiction is eventually reached.
n
(set theory) A function that maps distinct x in the domain to distinct y in the codomain; formally, a f: X → Y such that f(a) = f(b) implies a = b for any a, b in the domain.
adj
(set theory) Of a binary relation R on X: such that no element of X is R-related to itself.
n
(computing theory) An algorithm for finding the contiguous subarray within a one-dimensional numeric array which has the largest sum.
n
(mathematics, linear algebra, functional analysis) For a given function (especially a linear map between vector spaces), the set of elements in the domain which are mapped to zero; (formally) given f : X → Y, the set {x ∈ X : f(x) = 0}.
n
(computing theory) A heuristic algorithm for finding partitions of graphs, having important applications in the layout of digital circuits and components in VLSI.
n
(computing theory) Any of a family of functionally complete algebraic systems in which lambda expressions are evaluated according to a fixed set of rules to produce values, which may themselves be lambda expressions.
n
(mathematics) Formally, given two partially ordered sets A and B, the order ≤ on the Cartesian product A × B such that (a,b) ≤ (a′,b′) if and only if a < a′ or (a = a′ and b ≤ b′).
n
(mathematics) A preorder on vectors of real numbers.
n
An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.
n
(mathematics) The absolute value of a complex number.
n
(order theory, mathematical analysis) A function f : X→Y (where X and Y are posets with partial order "≤") with either: (1) the property that x ≤ y implies f(x) ≤ f(y), or (2) the property that x ≤ y implies f(y) ≤ f(x).
n
(set theory) A small model of (a fragment of) Zermelo-Fraenkel set theory with desirable properties (depending on the context).
n
(set theory) A generalized type of set in which multiple occurrences of an element are permitted.
n
(statistics) A lemma stating that when performing a hypothesis test between two point hypotheses H₀: θ = θ₀ and H₁: θ = θ₁, then the likelihood-ratio test which rejects H₀ in favour of H₁ when 𝛬(x)=(L(𝜃₀∣x))/(L(𝜃₁∣x))≤𝜂 where P(𝛬(X)≤𝜂∣H_0)=𝛼 is the most powerful test of size α for a threshold η.
n
(artificial intelligence, computing) A theorem that implies that no single machine learning algorithm is universally the best-performing algorithm for all problems.
n
(mathematics) An operator which modifies its operand, and which therefore is not the identity.
n
(set theory) The empty set.
adj
(mathematics, of a function) Taking no entries; having trivial domain; having the arity of zero.
n
(mathematics) The difference between the rank of a matrix and the number of columns it has; the dimension of the nullspace of a matrix.
n
(computing) The study of numerical analysis algorithms to solve mathematical problems in the field of linear algebra.
n
(mathematics) Any function whose value changes sign if the independent variable changes sign i.e. f(-x) = -f(x)
n
(mathematics) A set of operations, each one having a fixed finite number of arguments and one output, which can be composed with others.
n
(mathematics) A partially ordered set.
n
(number theory) function that represents the number of possible partitions of a natural number.
n
(mathematics, combinatorics) An ordering of a finite set of distinct elements.
adj
(mathematics) Occurring or true for each point of a given set.
adj
(mathematics) Describing an integer whose first digits are divisible by the numbers of digits concerned
n
(mathematics) The study of harmonic functions.
n
Alternative spelling of power set [(set theory, of a set S) The set whose elements comprise all the subsets of S (including the empty set and S itself).]
adj
(mathematics) Of a function, capable of being constructed from the zero function, successor function, and projection functions, by a finite number of applications of composition and recursion.
n
(set theory) A preorder.
n
(set theory) The original form of forcing, starting with a model M of set theory in which the axiom of constructibility, V = L, holds, and then building up a larger model M[G] of Zermelo-Fraenkel set theory by adding a generic subset G of a partially ordered set to M, imitating Kurt Gödel's constructible hierarchy.
n
(mathematics) A branch of mathematics which deals with patterns that inevitably arise in sufficiently large sets (i.e., subsets of some structure).
adj
(mathematics, arithmetic, not comparable) Of an algebraic expression, capable of being expressed as the ratio of two polynomials.
n
(mathematics) A number that can be expressed as the ratio of two integers.
adj
(mathematics) Of a relation R on a set S, such that xRx for all members x of S (that is, the relation holds between any element of the set and itself).
n
(mathematics, algebra) A branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
n
(computing theory) A theorem that establishes a limit on the extent to which an algorithm can decide whether certain mathematical expressions are equal.
n
(mathematics) The mathematical theory of sets.
n
(set theory) A set together with an equivalence relation.
n
(combinatorial game theory) A theorem stating that every impartial game under the normal play convention is equivalent to a nimber.
n
(mathematics) Synonym of Stirling number of the second kind
adj
based on, or inspired by, string theory
n
(mathematical analysis) Any of various methods for constructing generalized sums of series
n
(set theory) (real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y.
adj
(set theory) Of a relation R on a set S, such that xRy if and only if yRx for all members x and y of S (that is, if the relation holds between any element and a second, it also holds between the second and the first).
adj
(mathematical analysis) Alternative letter-case form of Tauberian [(mathematical analysis) Being or relating to Tauberian theorems, a class of theorems that are partial converses to Abelian theorems.]
n
(mathematics) Any value (variable or constant) or expression separated from another term by a space or an appropriate character, in an overall expression or table.
n
(mathematics) Alternative form of totative [(mathematics) A positive integer that is smaller than or equal to, and coprime to, another given positive integer.]
n
(set theory) Any cardinal or ordinal number which is larger than any finite, i.e. natural number; often represented by the Hebrew letter aleph (ℵ) with a subscript 0, 1, etc.
n
(set theory, order theory, of a binary relation R on a set X) The smallest binary relation on X that includes R and is transitive.
adj
(set theory) Such that, for all x and y in X, and for a binary relation R, exactly one of xRy, yRx or x=y holds.
n
(set theory) A finite sequence of terms.
adj
(mathematics) Of a binary relation: such that every non-empty subset of the relation's domain has a minimal element with respect to the relation.
n
(mathematics) A question of whether an element of a certain group (or monoid or the like) is the identity, given an obscure representation of that element.
n
(set theory) The well-ordering theorem.
adj
(mathematics) Of or relating to Zermelo-Fraenkel set theory.
n
(mathematics) A branch of algebra which relates to the direct search for unknown quantities.
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