Nodes at W0, stub

A tag, a kind, a name, an inventory row, and a same_as or a source.

Ideas 1201–1350 of 6044.

Name	Kind	Subject
Bernoulli trial	Concept	Probability theory and stochastic processes
Null space	Concept	Linear and multilinear algebra; matrix theory
Heine–Borel theorem in finite-dimensional normed spaces	Theorem	Functional analysis
Composition factors	Concept	Group theory and generalizations
Projections are continuous	Proposition	General topology
Order of an inverse	Proposition	Group theory and generalizations
The continued fraction of a rational number terminates	Theorem	Number theory
The Gaussian integers are a Euclidean domain	Theorem	Number theory
The constructible numbers form a field closed under square roots	Theorem	Field theory and polynomials
Interior is open	Proposition	General topology
Determinant is multilinear in the rows	Proposition	Linear and multilinear algebra; matrix theory
Second isomorphism theorem	Theorem	Group theory and generalizations
Null space	Definition	Linear and multilinear algebra; matrix theory
Probability of the complement	Proposition	Probability theory and stochastic processes
Alternating sum of binomial coefficients	Theorem	Combinatorics
Dirichlet convolution of multiplicative functions is multiplicative	Theorem	Number theory
Angle between two vectors	Definition	Geometry
Product of two subgroups	Concept	Group theory and generalizations
Endomorphism	Definition	Linear and multilinear algebra; matrix theory
Linear congruence	Concept	Number theory
Expectation with respect to the binomial distribution	Proposition	Probability theory and stochastic processes
The exponential series has infinite radius of convergence	Proposition	Functions of a complex variable
Orthogonal complement of the orthogonal complement	Proposition	Functional analysis
Composition of relations	Concept	Mathematical logic and foundations
Centraliser	Definition	Group theory and generalizations
Internal direct product	Definition	Group theory and generalizations
Cumulant generating function	Definition	Probability theory and stochastic processes
Image of a set	Definition	Mathematical logic and foundations
Integral of a power	Proposition	Real functions
Arc length parametrisation	Concept	Differential geometry
Second derivative	Concept	Real functions
Derived series	Concept	Group theory and generalizations
Galois group of a polynomial	Concept	Field theory and polynomials
The sequence r^n tends to zero for \|r\| < 1	Example	Sequences, series, summability
Holomorphic functions with nonzero derivative are conformal	Proposition	Functions of a complex variable
Third Sylow theorem	Theorem	Group theory and generalizations
Orthogonal projection	Definition	Linear and multilinear algebra; matrix theory
Joint probability distribution	Definition	Statistics
Subspace metric	Concept	General topology
Reciprocal rule	Proposition	Real functions
Equivalence relation induced by a function	Definition	Mathematical logic and foundations
Holomorphic functions are infinitely differentiable	Corollary	Functions of a complex variable
Cayley–Hamilton theorem for linear maps	Theorem	Linear and multilinear algebra; matrix theory
Infimum	Concept	Order, lattices, ordered algebraic structures
Eigenvalues are the roots of the minimal polynomial	Theorem	Linear and multilinear algebra; matrix theory
The algebraic numbers form a field	Theorem	Number theory
Fundamental solution of Pell's equation	Concept	Number theory
Irrationality of pi	Theorem	Number theory
Matrix of a bilinear form	Concept	Linear and multilinear algebra; matrix theory
Dimension of the coordinate space	Proposition	Linear and multilinear algebra; matrix theory
Implicit differentiation	Concept	Real functions
Derivative function	Concept	Real functions
Euclidean domains are principal ideal domains	Theorem	Commutative algebra
The Galois group has order at most the degree	Theorem	Field theory and polynomials
Contraction mapping	Concept	Operator theory
Transitive action	Definition	Group theory and generalizations
Von Dyck's theorem	Theorem	Group theory and generalizations
Derivative of a map into a product	Proposition	Real functions
Number of odd-degree vertices is even	Corollary	Combinatorics
Asymptotic equivalence	Concept	Approximations and expansions
In a UFD irreducible elements are prime	Theorem	Commutative algebra
Upper and lower Darboux sums	Definition	Real functions
Recurrence for derangements	Theorem	Combinatorics
Semisimple endomorphism	Definition	Linear and multilinear algebra; matrix theory
The reals form an ordered field	Theorem	Field theory and polynomials
The group of units of Z/pZ is cyclic	Theorem	Number theory
Frattini argument	Lemma	Group theory and generalizations
Dimension of a subspace	Proposition	Linear and multilinear algebra; matrix theory
Every element of a finite field of order q satisfies x^q = x	Proposition	Field theory and polynomials
Order of a zero	Concept	Functions of a complex variable
Picard–Lindelöf hypotheses	Concept	Ordinary differential equations
Convergent sequences are Cauchy	Proposition	Sequences, series, summability
Coefficient of a power series	Concept	Commutative algebra
Continuity of the sum of a uniformly convergent series of functions	Corollary	Sequences, series, summability
Abelian groups are solvable	Proposition	Group theory and generalizations
Content of a polynomial	Concept	Commutative algebra
Connected set	Definition	General topology
Derived series	Definition	Group theory and generalizations
Supremum	Concept	Order, lattices, ordered algebraic structures
Type I and type II errors	Definition	Statistics
Fraction in lowest terms	Theorem	Number theory
Compact set	Concept	General topology
Annihilator of a subspace	Definition	Linear and multilinear algebra; matrix theory
Universal property of the quotient ring	Theorem	Associative rings and algebras
Compact subsets of a metric space are bounded	Proposition	General topology
Symmetry of binomial coefficients	Theorem	Combinatorics
pi is greater than 3	Proposition	Number theory
A linear isometry preserves the inner product	Proposition	Linear and multilinear algebra; matrix theory
Dimension of a tensor product	Corollary	Linear and multilinear algebra; matrix theory
Geometric series as a power series	Example	Commutative algebra
A linear map is determined by its values on a basis	Proposition	Linear and multilinear algebra; matrix theory
Integers modulo a prime form a field	Theorem	Number theory
Characterization of the floor	Proposition	Real functions
Divisibility by 3	Proposition	Number theory
Gcd of Fibonacci numbers	Theorem	Number theory
Dyck word	Definition	Computer science
One-sided derivative	Concept	Real functions
Limit of a sum of sequences	Proposition	Sequences, series, summability
Focus of a conic	Concept	Geometry
Cluster point of a sequence	Definition	Sequences, series, summability
Indicator function	Concept	Mathematical logic and foundations
Arccosine	Definition	Special functions
Cesàro means of a convergent sequence converge	Proposition	Sequences, series, summability
Space of matrices	Example	Linear and multilinear algebra; matrix theory
Generating function of a sum of independent random variables	Proposition	Probability theory and stochastic processes
Composition factors	Definition	Group theory and generalizations
Stabiliser	Definition	Group theory and generalizations
Incircle	Definition	Geometry
Submodule	Definition	Associative rings and algebras
Picard iteration	Concept	Ordinary differential equations
Limit of the cumulative distribution function at infinity	Proposition	Probability theory and stochastic processes
Logarithm is the inverse of the exponential	Theorem	Special functions
Proper metric space	Concept	General topology
Homogeneous first-order equation	Concept	Ordinary differential equations
Complex power	Concept	Special functions
Damped harmonic oscillator	Example	Mechanics of particles and systems
Trace of a linear map	Definition	Linear and multilinear algebra; matrix theory
Cantor set is homeomorphic to the space of binary sequences	Theorem	General topology
Fixed points of an action	Concept	Group theory and generalizations
Focus of a conic	Definition	Geometry
Orthonormal family	Concept	Linear and multilinear algebra; matrix theory
Every infinite set has a countably infinite subset	Theorem	Mathematical logic and foundations
Image of an intersection	Proposition	Mathematical logic and foundations
Distributivity of matrix multiplication	Proposition	Linear and multilinear algebra; matrix theory
A continuous nowhere differentiable function	Counterexample	Real functions
Structure theorem for finitely generated abelian groups	Theorem	Group theory and generalizations
A nontrivial finite p-group has nontrivial centre	Theorem	Group theory and generalizations
Power-reduction formula for cosine	Corollary	Special functions
Addition of natural numbers	Concept	Mathematical logic and foundations
Wedge product of forms	Definition	Linear and multilinear algebra; matrix theory
Size of an orbit times the size of the stabiliser	Corollary	Group theory and generalizations
Variation of constants formula for linear systems	Theorem	Ordinary differential equations
Image of a homomorphism	Concept	Group theory and generalizations
Smallest prime factor	Definition	Number theory
Convergent sequences are bounded	Proposition	Sequences, series, summability
Inverse of a product	Proposition	Linear and multilinear algebra; matrix theory
Biconditional	Concept	Mathematical logic and foundations
Order of the group of units of Z/nZ is Euler's totient	Proposition	Number theory
Algebraic multiplicity	Definition	Linear and multilinear algebra; matrix theory
External direct sum	Concept	Linear and multilinear algebra; matrix theory
Chain	Concept	Order, lattices, ordered algebraic structures
Continuity in R^n	Definition	Real functions
Derivative of tangent	Proposition	Special functions
Dirichlet convolution formula	Proposition	Number theory
Path component	Definition	General topology
Product rule in several variables	Proposition	Real functions
Basis of a tensor product	Theorem	Linear and multilinear algebra; matrix theory
Closure is the smallest closed superset	Proposition	General topology
Split polynomial	Definition	Field theory and polynomials
Pendulum equation	Example	Mechanics of particles and systems