(set theory) The set that contains exactly those elements belonging to the universal set but not to a given set.

(mathematics) A subbranch of combinatorics that concerns additive problems expressed using sumsets.

(algebra) positive; not negative

(set theory, order theory) A subset, A, of a partially ordered set, (P, ≤), such that no two elements of A are comparable with respect to ≤.

(logic) arithmetical hierarchy

(logic) A set of natural numbers that can be defined by a formula of first-order Peano arithmetic.

(mathematics) The science of numbers; basic arithmetic

(logic, mathematics, computer science) The number of arguments or operands a function or operation takes. For a relation, the number of domains in the corresponding Cartesian product.

(set theory) A weaker form of the axiom of choice that states that every countable collection of nonempty sets must have a choice function; equivalently, the statement that the direct product of a countable collection of nonempty sets is nonempty.

(set theory, order theory, "on" a set A) A subset of the Cartesian product A×A (the set of ordered pairs (a, b) of elements of A).

A 20th-century French movement aiming to found all of mathematics on set theory.

(set theory) The paradox that supposing the existence of a set of all ordinal numbers leads to a contradiction; construed as meaning that it is not a properly defined set.

(mathematics, physics) A set of spacetimes that have a causality relationship

(mathematics, set theory, order theory) A totally ordered set, especially a totally ordered subset of a poset.

(mathematics) A form (expression) that does not use limits, implicitly or explicitly.

(economics) A theorem stating that, if trade in an externality is possible and there are sufficiently low transaction costs, bargaining will lead to a Pareto efficient outcome regardless of the initial allocation of property.

(order theory) Of a subset of a partially ordered set; containing elements at least as late as any given element of the set, relative to the given partial order.

(set theory) Such that, for all x and y in X, and for a binary relation R, either or both of xRy and yRx hold(s).

The quality of being coprime.

(set theory, countable) A relation.

(set theory, of a set) That is both countable and infinite; having the same cardinality as the set of natural numbers; formally, such that a bijection exists from ℕ to the set.

(mathematics) a positive integer

Alternative spelling of coefficient [(mathematics) A constant by which an algebraic term is multiplied.]

A thesis which claims the existence of an analogy or correspondence between — on the one hand — constructive mathematical proofs and programs (especially functions of a typed functional programming language), and — on the other hand — between formulae (proven by the aforementioned proofs) and types (of the aforementioned functions).

(mathematics) The different ideal.

(informal) Discrete mathematics.

(mathematics) A union of sets which are already pairwise disjoint.

(set theory) The property of an ordered set such that its elements can be listed in an order such that, for every element, the element is irreducible (has exactly one upper or lower cover) in the subset consisting of that element and all subsequent elements.

(set theory) A binary relation that is reflexive, symmetric and transitive.

(mathematics, of an integer or polynomial etc) Able to be factorized.

(mathematics) An element of the range of a function. (Or, employing the "machine" metaphor, it is one of the "outputs" of a function.)

(chiefly mathematics) A theorem (or, in non-mathematical fields, a commonly accepted hypothesis) considered to be of central importance to a specified field.

a form of logic based on the concept of a fuzzy set

A theorem stating that, for any deterministic process of collective decision, at least one of the following three properties must hold: (i) the process is dictatorial, i.e. there exists a distinguished agent who can impose the outcome; (ii) the process limits the possible outcomes to two options only; (iii) the process encourages agents to think strategically: once an agent has identified their preferences, they have no action at their disposal that would best defend their opinions in any situation.

A theorem dealing with deterministic ordinal electoral systems that choose a single winner, stating that for every voting rule, one of the following three things must hold: (i) the rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner; or (ii) the rule limits the possible outcomes to two alternatives only; or (iii) the rule is susceptible to tactical voting: in certain conditions some voter's sincere ballot may not defend their opinion best.

A parody of the three laws of thermodynamics in terms of a person playing a game: (1) you can't win; (2) you can't break even; (3) you can't even get out of the game.

(mathematics) Relating to or using graph theory.

(logic) A number uniquely assigned to each symbol, and to each well-formed formula of some formal language.

(logic) Gödel numbering

(logic) A function which replaces a variable bound by a universal quantifier which lies in the scope of an even number of logical negations; such function is a function of the remaining bound variables whose scope contain the given variable (being replaced).

(logic) A fundamental result of mathematical logic, essentially allowing a certain kind of reduction of first-order logic to propositional logic.

(algebra) An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this second element.

(electrical engineering) On a Karnaugh map: a set of ones (whose quantity is a power of two) which are related by adjacency (i.e., the set is connected, if the Karnaugh map is considered to be a graph which "wraps around" its edges, like a torus; and all elements of the subgraph induced by the set have the same degree). Equivalently, in terms of Boolean algebra, a product term which, when true, always implies that the given Boolean function is true.

(informal) The proposition that a monkey hitting typewriter keys at random is bound to produce meaningful text (such as a work by William Shakespeare), given an infinite amount of time.

(arithmetic) A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.

(mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign.

(mathematics) Pertaining to a generalization of alphabetical order applied to sets such that, for each pair of sets, their relative ordering is the order obtained if you remove their common (shared) elements and compare the last element in each remaining subset.

(mathematics) A related function that, given the output of the original function returns the input that produced that output.

(set theory) Of a binary relation, to have every element of the left set occur at least once: ∀a∈A∃b∈B:(a,b)∈R⊆A⨯B

(mathematical analysis) The set of values x for which a real-valued function f(x) is equal to a given constant.

(mathematics) Given sets (A₁, A₂, ..., Aₙ) and their total orderings (<₁, <₂, ..., <ₙ), the order <ᵈ of A₁ × A₂ × ... × Aₙ such that (a₁, a₂, ..., aₙ) <ᵈ (b₁,b₂, ..., bₙ) iff (∃m > 0) (∀ i < m) (aᵢ = bᵢ ) and (aₘ <ₘ bₘ )

(set theory, order theory) total order

(mathematics) Relating to logic and mathematics (or to mathematical logic)

The use of mathematics to construct formal theories about society.

Obsolete form of mathematics. [An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.]

The study of learning.

(informal, Commonwealth, rarely Canada) Clipping of mathematics. [An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.]

(computing) Acronym of not a number: applied to numeric values that represent an undefined or unrepresentable value, such as zero divided by itself.

(mathematics) A negative quantity.

(mathematics, set theory, measure theory) A set that is small enough that it can be ignored for some purpose.

(US, education, historical) A dramatic and short-lived change in the teaching of mathematics in grade schools in the 1960s, focusing on abstract topics such as symbolic logic, to the detriment of simple arithmetic etc.

(set theory) Of a set, containing at least one element; not the empty set.

(electrical engineering) On a Karnaugh map: a prime implicant which does not cover any 1 which cannot covered by some other prime implicant.

(arithmetic) An empty sum.

(mathematics, computing) Describing an action which has no side effect. Queries are typically nullipotent: they return useful data, but do not change the data structure queried. Contrast with idempotent.

(mathematics) An additive inverse.

(order theory) A partially ordered set.

(set theory) In the context of sets equipped with an order (especially, the context of totally ordered sets), the characteristic of being a member of some equivalence class of such sets under the equivalence relation "existence of an order-preserving bijection".

(mathematics, set theory, of a collection of two or more sets) Let A_𝜆_(𝜆∈𝛬) be any collection of sets indexed by a set 𝛬. We call the indexed collection pairwise disjoint if for any two distinct indices, 𝜆,𝜇∈𝛬, the sets A_𝜆 and A_𝜇 are disjoint.

(set theory, order theory) A binary relation that is reflexive, antisymmetric, and transitive.

(set theory) A partial order.

(set theory, order theory, of a set) Equipped with a partial order; when the partial order is specified, often construed with by.

(set theory, order theory, formally) The ordered pair comprising a set and its partial order.

(geometry, number theory) A proposition affirming the possibility of finding such conditions as will render a certain determinate problem indeterminate or capable of innumerable solutions.

(set theory, of a set S) The set whose elements comprise all the subsets of S (including the empty set and S itself).

(mathematics) A easy and concise method of applying the rules of arithmetic to questions which occur in trade and business.

(mathematics) A matrix that has a smaller condition number than another

(set theory, order theory) A binary relation that is reflexive and transitive.

(mathematics, set theory) A binary relation that is transitive, total, and well-founded.

(electrical engineering) A group of related 1's (implicant) on a Karnaugh map which is not subsumed by any other implicant in the same map. Equivalently (in terms of Boolean algebra), a product term which is a "minimal" implicant in the sense that removing any of its literals will yield a product term which is not an implicant (but beware: on a Karnaugh map it would appear "maximal").

(mathematics) Of, pertaining to, or derived using probability.

(set theory) A class which is not a set.

(computer science) A lemma which states that for a language to be a member of a language class any sufficiently long string in the language contains a section that can be removed or repeated any number of times with the resulting string remaining in the language, used to determine if a particular language is in a given language class (e.g. not regular).

(set theory) Of a relation ~ on a set S: such that every element that is related to some element is also related to itself, i.e. ∀x,y∈S: x~y ⇒ x~x ∧ y~y.

(set theory) A set of ordered tuples.

(set theory, of set A "in" set B) The set containing exactly those elements belonging to B but not to A.

(computing theory) A theorem stating that all nontrivial semantic properties of programs are undecidable.

(set theory) Of a binary relation, to have every element of the right set occur at least once: ∀b∈B∃a∈A:(a,b)∈R⊆A⨯B

(set theory) The paradox that a set defined to contain all sets which do not contain themselves can neither consistently contain itself nor not contain itself.

(mathematics) univalent (analytic and one-to-one) in a given region, sometimes qualified with the stipulation that the function is 0 at 0 and has a slope there equal to 1 (see w:Koebe function)

(mathematics, logic) Denoting the second in a numerical sequence of models, languages, relationships, forms of logical discourse etc.

(set theory) A collection of zero or more objects, possibly infinite in size, and disregarding any order or repetition of the objects which may be contained within it.

(mathematics) In a manner which uses set theory

(set theory) A mathematical notation for describing a set by specifying the properties that its members must satisfy.

Alternative spelling of set-theoretic [(mathematics) Of, relating to or using set theory.]

Alternative spelling of set theoretically [(mathematics) In a manner which uses set theory]

(mathematics) In terms of a set or sets.

(mathematics, of a function) Having derivatives of all finite orders at all points within the function’s domain.

The problem of finding a stable matching between two equal-sized sets of elements, given an ordering of preferences for each element.

(mathematics) a set of equations required to be satisfied simultaneously or considered as a whole

(mathematics) A field of study attempting to exhaustively describe a particular class of constructs.

(set theory, order theory) A partial order, ≤, (a binary relation that is reflexive, antisymmetric, and transitive) on some set S, such that any two elements of S are comparable (for any x, y ∈ S, either x ≤ y or y ≤ x).

(mathematics, rare) A total order.

(set theory, of a relation on a set) Having the property that if an element a is related to b and b is related to c, then a is necessarily related to c.

(uncountable) A branch of mathematics dealing with equational classes of algebras, where similar theorems from disparate branches of algebra are unified.

(computing) Not accepting negative numbers; having only a positive absolute value.

(set theory, order theory, transitive) To impose a well-order on (a set).

(mathematics) The fact that, in some circumstances, the probability of an event can only be zero or one and not any intermediate value.