n
(algebra) A set of equivalence classes which partition the disjoint union of the members of a direct system; each equivalence class being a sort of “drainage basin” of the mappings (of the morphisms) of the direct system, if these are analogically considered as “rivers”. (If i
n
(mathematics) A type of infinity in the complex plane that has a defined angle θ but an infinite absolute value r.
adj
(mathematics) Proportional to a constant multiple of an independent variable.
n
(physics) A mathematical notation using indices to label the components of vectors and tensors.
n
(mathematics) The result of operating any number of times upon a quantic with the operator (x'd/dx + y'd/dy + ... + z'd/dz).
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(mathematics) One of the products arising from the multiplication of two or more values by the same value.
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(mathematics) A formula connecting a finite sum of products to a finite continued fraction: a_0+a_0a_1+a_0a_1a_2+⋯+a_0a_1a_2⋯a_n= cfrac a_0 1- cfrac a_1 1+a_1- cfrac a_2 1+a_2- cfrac ddotsddots cfrac a_n-1 1+a_n-1- cfrac a_n 1+a_n,.
n
(mathematics) A constant, denoted γ and recurring in analysis and number theory, that is defined as the limiting difference between the harmonic series and the natural logarithm and has the approximate value 0.57721566.
n
(mathematics) The number by which a value (called the base) is said to be raised to a power in exponentiation: for example, the 3 in 2³=8.
n
(mathematics) Any function that has an exponent as an independent variable.
n
(mathematics) A type of equation which includes a variable located in the exponent; for example, eˣ=1,.
n
(mathematics, arithmetic, countable) A mathematical problem involving exponentiation.
n
(mathematics) A polynomial with few monomials.
n
(mathematics) The numeric value of the integral over the positive real numbers of the reciprocal of the gamma function, F=∫₀ ᪲1/(𝛤(x))dx=2.8077702420285....
n
(mathematical analysis) A sequence in which each term except the first is obtained from the previous by multiplying it by a constant value, known as the common ratio of the geometric progression.
n
(mathematical analysis) Any infinite series whose terms are in geometric progression; any series of the form a+ar+ar²+ar³⋯=a∑ᵢ₌₀ ᪲rⁱ.
n
(geometry) The irrational number (approximately 1.618), usually denoted by the Greek letter φ (phi), which is equal to the sum of its own reciprocal and 1, or, equivalently, is the square root of the sum of itself and 1.
n
(combinatorics) A family of order k of sets, such that any minimal subfamily with an empty intersection has k or fewer sets in it.
n
(mathematics) a polynomial such that the sum of the exponents of the variables is the same for every term.
adj
(mathematics) Pertaining to a generalization of computability theory focusing on certain sets of natural numbers.
n
(mathematics) The result of multiplying a given number of consecutive integers from 1 to the given number, each raised to its own power.
adj
(mathematics) Pertaining to a generalization of the Fibonacci sequence that derives each term as the sum of the previous r terms for any r ≥ 1.
n
(mathematics, non-standard analysis) A hyperreal number equal to its own integer part.
adj
(mathematics, of a sequence) Converging very quickly to a limit so that the ratio of adjacent terms tends to zero.
n
(mathematics) One of a sequence of operations for compounding numbers that increase in growth iteratively.
adj
(mathematics) Being a hyperperfect number.
adj
(mathematics, of a number) Belonging to an extension of the real numbers containing those that cannot be produced by repeatedly adding 1; hence infinite.
adj
(mathematics, of a number) Having no real part; that part of a complex number which is a multiple of √ (called imaginary unit).
n
(complex analysis, strict sense) A number of the form bi, where b is any real number and i denotes the imaginary unit.
n
(complex analysis) Of a complex number a + bi, where a and b are real numbers, the value b.
n
(mathematical analysis) Any expression that represents the addition a countably infinite number of ordered summands, often explicitly indexed by the positive or nonnegative integers.
n
(mathematics) Any real number that cannot be expressed as a ratio of two integers.
n
(mathematics) Such a polynomial
n
(mathematics) An alternative version of i, the positive square root of -1; used in the context of electronics.
n
(mathematics) In complex dynamics, a set consisting of values generated by a mathematical function such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values.
n
multiplication by means of the Karatsuba algorithm
n
(mathematics, set theory) A tree (T, <) of height ω₁, each of whose levels is at most countable, and has at least ℵ₂ branches.
n
Alternative letter-case form of L'Hôpital's rule [(mathematics) The rule that the limit of the ratio of two functions equals the limit of the ratio of their derivatives, usable when the former limit is indeterminate and the latter limit exists.]
n
(mathematics) Any of a class of coefficients expressing rising factorials in terms of falling factorials.
n
(physics, countable and uncountable) A lattice model, a mathematical model based on a lattice (discrete subgroup of Rⁿ); the study of such models.
n
A power series generalising Taylor series, in which the exponents may be positive or negative integers.
n
(number theory) A lemma used to calculate the p-adic order of differences and sums of perfect powers.
n
In Boolean algebra, a product term, with a value of 1, in which each variable appears once (in either its complemented or uncomplemented form, so that the value of the product term becomes 1).
n
(fractal geometry, mathematics) A fractal element.
n
(computing) The operation or function that returns the remainder of one number divided by another.
n
(mathematics) The base with respect to which a congruence is computed.
n
(mathematics) A single term consisting of a product of numbers and variables with positive integer exponents.
n
(algebra) A partition of a set into disjoint subsets such that each subset contains an even number of elements, and that if those elements are ordered, they divide the subset into ranges (1st to 2nd element, 3rd to 4th element, and so on) such that no element from another subset appears in any of the ranges.
n
(mathematics) A multivalued function.
n
(mathematics) A set with repeated elements that are indistinguishable from one another.
n
(mathematics) A mapping f:Xⁿ→𝒫(X) for some n∈ℕ₀.
n
(mathematics, obsolete) A partial product, i.e., the result of one step of a full multiplication algorithm.
adj
(algebra) Having multiplication as an operator.
n
(mathematics) A set of formulas that have n free variables of a certain sort
n
(mathematics) Any of the 24 positive definite even unimodular lattices of rank 24.
n
(mathematics, algebra) A name or term.
n
(algebra) An algebra over a field whose bilinear product is not necessarily associative.
adj
(mathematics) Not connected: having more than one connected component.
n
Alternative form of non-hypotenuse number [(mathematics) A natural number whose square cannot be written as the sum of two nonzero squares.]
n
(mathematics) An integer that is never a value of Euler's totient function.
n
(mathematics) A zero-growth isocline, encountered in a system of ordinary differential equations.
n
(algebra) A norm on a vector space which is defined over a field equipped with a discrete valuation (a generalisation of p-adic absolute value).
n
(mathematics) The "best" approximation of a function by a rational function of given order. Under this technique, the approximant's power series agrees with the power series of the function it is approximating.
n
Alternative form of Pell's equation [(number theory) The Diophantine equation x²-my²=1 for a given integer m, to be solved in integers x and y.]
n
(number theory) The Diophantine equation x²-my²=1 for a given integer m, to be solved in integers x and y.
n
(mathematics) A representation of a complex number in terms of a complex exponential.
adj
(mathematics) Relating to a certain type of graph, complying with the theorem (pluperfect graph theorem) discovered by D. R. Fulkerson in 1970.
n
(mathematics) A meromorphic function on ℂ, defined as the (m+1)-th derivative (for a given order m) of the logarithm of the gamma function.
adj
(algebra) Able to be described or limited by a polynomial.
n
(mathematics) Any function whose value is the solution of a polynomial; an element of a subring of the ring of all functions over an integral domain, which subring is the smallest to contain all the constant functions and also the identity function. (If the polynomial is multivariate then there is a different identity function corresponding to each variable.)
n
(mathematics) A function of the form f(x_1,x_2,…,x_n)=∑ₖ₌₁ᴷc_kx_1^(a_1k)⋯x_n^(a_nk), where all the coordinates x_i and coefficients c_k are positive real numbers, and the exponents a_ik are real numbers.
n
A product of equal factors (and generalizations of this notion): xⁿ, read as "x to the power of n" or the like, is called a power and denotes the product x⨯x⨯⋯⨯x, where x appears n times in the product; x is called the base and n the exponent.
n
(mathematics) A function where the independent variable is raised to a particular real number power.
n
(mathematics) A chain of exponentiations, or raising to powers, of the form a^(aa...); tetration.
adj
(complex analysis) Of a number, having real part equal to zero.
n
(mathematics) A number (real or complex) which is a solution to an equation of the form x²+Bx+C=0 for some integers B and C. For example 42, or 2+3i, or 1+√/2.
n
(mathematics) The number or expression whose square root or other root is being considered.
n
(mathematics) A real number.
adj
(mathematics) Used to describe a mathematical entity, like a function, that takes values from the real numbers (as opposed to, for instance, from the complex numbers).
n
(mathematics) A number which is the product of two consecutive integers
adj
(mathematics, of a matrix) For which the limit lim _(k→∞) bold Tᵏ exists.
n
(algebra, databases) A type of join in relational algebra, denoted by ⋉ or ⋊.
adj
(mathematics) Of a ring over which every finitely generated left module has a projective cover.
n
(algebra) An exact sequence of precisely three nontrivial objects (e.g., modules).
n
(mathematics) A permutation in which, for all k, the subsequence of the smallest k elements has no three consecutive elements in decreasing order.
n
(mathematics) A set with exactly one element.
n
(mathematics) An element of the two-dimensional algebra over the field of real numbers which contains an element ȷ ≠ 1 satisfying ȷ² = 1.
n
(mathematics) The number which, when squared, yields another number.
n
(mathematics) Any of a certain series of numbers that occur in the Laurent series expansion of the Riemann zeta function.
adj
(mathematics) Expressed by the square root; said of ratios.
n
(mathematics) A subgraph that is a forest.
adj
(mathematics) Describing a function that grows more slowly than a linear one.
n
(mathematics) A natural number x, with the property that x = bⁱy for some y that is not multiple of b.
n
(mathematics) A quiver that forms part of a larger quiver.
n
(set theory, of a set S) A set A such that every element of A is also an element of S.
n
(mathematics) A set which serves as the codomain of a characteristic function.
n
(mathematics) A subset of a variety which is itself a variety.
n
(mathematics) The larger code that a subcode is part of
adj
(mathematics, set theory) Being a type of large cardinal with a variety of reflection properties.
n
(mathematics) A congruence modulo some power of a prime
adj
(mathematics, of a real-valued function f on the non-negative real numbers) Having the properties that f(0) = 1 and ∀ g,h ≥ 0: f(g)f(h) ≤ f(g+h) .
n
(mathematics) A product of factorials, such that the superfactorial of a number n is 1! × 2! × 3! × ... × n!.
adj
(mathematics, obsolete) Of a natural number, being larger than another natural number by a unit fraction of that smaller number.
n
(mathematics) For some value n, a string that contains each permutation of n symbols as a substring.
adj
(computing, mathematics) Describing an algorithm whose execution time is not limited by a polynomial
adj
(mathematics) Of or pertaining to the superreal numbers, a generalization of the hyperreal numbers.
n
(arithmetic) An irrational number, especially one expressed using the √ symbol.
n
(mathematics) Any element of a field equivalent to the real numbers augmented with infinite and infinitesimal numbers (respectively larger and smaller (in absolute value) than any positive real number).
n
(mathematics) Any function, of multiple variables, whose value is independent of the order of the variables, i.e. f(a,b) = f(b,a).
n
(mathematics) A rational integral function of the invariants of a quantic that vanishes when expressed as a function of the coefficients.
n
(algebra, field theory, of a field extension) Given a field extension L / K, the largest cardinality of an algebraically independent subset of L over K.
n
(mathematics) any irrational number that is not an algebraic number
n
(set theory, of a set X) The smallest transitive set that contains X.
n
(mathematics) A variant of the Fibonacci sequence in which the preceding three terms, rather than the preceding two, are summed at each iteration.
n
(mathematics) The special case of an ultraproduct where all factors are equal.
n
(mathematics) An infinite product of nested radicals representing the constant pi: specifically, 2/𝜋=(√2)/2·√/2·√/2⋯
n
(mathematics) An infinite product that approximates half of pi: 𝜋/2=∏ₙ₌₁ ᪲(4n²)/(4n²-1)=∏ₙ₌₁ ᪲((2n)/(2n-1)·(2n)/(2n+1))\[6pt]= Big (2/1·2/3 Big )· Big (4/3·4/5 Big )· Big (6/5·6/7 Big )· Big (8/7·8/9 Big )·;⋯\.
n
(algebra) A way of representing an exterior product using a wedge symbol: ∧.
n
(graph theory) The function for which the Zarankiewicz problem seeks a formula: z(m, n; s, t), denoting the largest possible number of edges in a bipartite graph G = (U, V, E) for which |U| = m and |V| = n, but which does not contain a subgraph of the form K_(s,t).
n
A tensor with all entries equal to zero; where any pattern of covariant and contravariant indices have all components equal to 0.
n
(mathematics) a vector whose value in every dimension is zero. i.e. ⃑0=<0,0,…,0>
n
(mathematics) The value of a particular zeta function
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