Nodes at W0, stub

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

Ideas 901–1050 of 6044.

Name	Kind	Subject
Cardinality of the power set	Proposition	Mathematical logic and foundations
The medians meet at the centroid	Theorem	Geometry
Quotient of continuous functions is continuous	Proposition	Real functions
Wedge product of forms	Concept	Linear and multilinear algebra; matrix theory
Curl-free field that is not conservative	Counterexample	Real functions
Angles in the same segment are equal	Corollary	Geometry
Ideal generated by a subset	Concept	Commutative algebra
Decimal expansion as a series	Example	Sequences, series, summability
Bijection principle	Theorem	Combinatorics
Fundamental theorem of symmetric polynomials	Theorem	Combinatorics
Area under a curve	Concept	Real functions
Integral of sine	Proposition	Real functions
Units of Z/nZ are the residues coprime to n	Proposition	Number theory
Second derivative test in several variables	Theorem	Calculus of variations and optimal control; optimization
Divergence theorem on a rectangle in the plane	Proposition	Real functions
Fundamental matrix	Concept	Ordinary differential equations
Limit inferior	Definition	Sequences, series, summability
The order of a finite field is a prime power	Theorem	Field theory and polynomials
Taylor's theorem with the Lagrange remainder	Theorem	Approximations and expansions
Changing the order of integration	Proposition	Real functions
Galton–Watson process	Definition	Probability theory and stochastic processes
Product of power series	Theorem	Commutative algebra
Every finite tree with at least two vertices has a leaf	Lemma	Combinatorics
Rule of Sarrus	Proposition	Linear and multilinear algebra; matrix theory
Plane	Definition	Geometry
Abelianisation	Definition	Group theory and generalizations
Rectifiable curve	Concept	Real functions
Interior is the largest open subset	Proposition	General topology
Markov property	Definition	Probability theory and stochastic processes
Induction on the integers	Theorem	Number theory
Union of open sets is open	Proposition	General topology
Taylor polynomial	Definition	Approximations and expansions
Sum of a series	Concept	Sequences, series, summability
Differentiable function of several variables	Concept	Real functions
Solutions for distinct real roots	Theorem	Ordinary differential equations
Thomae's function	Example	Real functions
Second isomorphism theorem for rings	Theorem	Associative rings and algebras
Random experiment	Concept	Probability theory and stochastic processes
A sequence converges iff its liminf and limsup agree	Proposition	Sequences, series, summability
Order on the natural numbers	Concept	Mathematical logic and foundations
Centre of mass	Concept	Real functions
Eigenvectors with distinct eigenvalues are linearly independent	Theorem	Linear and multilinear algebra; matrix theory
Generalised Stokes theorem	Theorem	Global analysis, analysis on manifolds
Archimedean ordered field	Definition	Field theory and polynomials
Coefficient matrix	Concept	Linear and multilinear algebra; matrix theory
Rearrangement of a series	Definition	Sequences, series, summability
Solutions for repeated roots	Theorem	Ordinary differential equations
One-sided derivative	Definition	Real functions
Totient of a prime	Proposition	Number theory
Eigenvalues of a positive definite matrix are positive	Theorem	Linear and multilinear algebra; matrix theory
Injective iff it has a left inverse	Proposition	Mathematical logic and foundations
Polar form of a quadratic form	Concept	Linear and multilinear algebra; matrix theory
Modulus is multiplicative	Proposition	Functions of a complex variable
Student's t-test	Concept	Statistics
Mean value property	Theorem	Potential theory
Norm of a Gaussian integer	Concept	Number theory
Quotient map	Definition	Linear and multilinear algebra; matrix theory
Fixed field	Concept	Field theory and polynomials
Euclidean isometry	Concept	Geometry
Solutions of Pell's equation are powers of the fundamental solution	Theorem	Number theory
Existence of nth roots by the intermediate value theorem	Example	Real functions
Cycle type	Concept	Group theory and generalizations
Conjugacy classes of the symmetric group correspond to cycle types	Theorem	Group theory and generalizations
The symmetric group on five or more letters is not solvable	Theorem	Group theory and generalizations
Characteristic polynomial of a linear map	Concept	Linear and multilinear algebra; matrix theory
Congruence is compatible with powers	Corollary	Number theory
Lyapunov's stability theorem	Theorem	Ordinary differential equations
Associativity of composition	Proposition	Mathematical logic and foundations
Kuratowski's theorem	Theorem	Combinatorics
Discrete random variable	Definition	Probability theory and stochastic processes
Rearrangements of an absolutely convergent series have the same sum	Theorem	Sequences, series, summability
Endomorphism	Concept	Linear and multilinear algebra; matrix theory
Picard–Lindelöf hypotheses	Definition	Ordinary differential equations
Logarithm of a quotient	Corollary	Special functions
Primitive root of unity	Definition	Number theory
Composition of an integer	Definition	Combinatorics
Taylor's theorem in several variables	Theorem	Real functions
Reachability	Definition	Combinatorics
Limit of a function of several variables	Concept	Real functions
Determinant of a block triangular matrix	Proposition	Linear and multilinear algebra; matrix theory
Image of a linear map	Definition	Linear and multilinear algebra; matrix theory
Ratio formula for the radius of convergence	Proposition	Functions of a complex variable
Vector calculus identities	Theorem	Real functions
Converse relation	Definition	Mathematical logic and foundations
Continuity in R^n	Concept	Real functions
Sign is a homomorphism	Theorem	Group theory and generalizations
The cumulative distribution function determines the distribution	Theorem	Probability theory and stochastic processes
Parametrised curve	Definition	Differential geometry
Space of polynomials of bounded degree	Example	Linear and multilinear algebra; matrix theory
Eigenspaces of a self-adjoint operator are orthogonal	Proposition	Operator theory
The ring of integers	Example	Commutative algebra
Underdamped	Concept	Mechanics of particles and systems
Cauchy's estimates	Corollary	Functions of a complex variable
Abelian simple groups have prime order	Proposition	Group theory and generalizations
Kernel of a ring homomorphism	Concept	Associative rings and algebras
Convolution theorem for the Laplace transform	Theorem	Integral transforms, operational calculus
Function of several variables	Concept	Real functions
Subgroups of abelian groups are normal	Proposition	Group theory and generalizations
Order of the general linear group over a finite field	Theorem	Group theory and generalizations
Weierstrass approximation theorem	Theorem	Approximations and expansions
Multiplication of natural numbers	Definition	Mathematical logic and foundations
Estimate for approximate solutions	Theorem	Ordinary differential equations
Split polynomial	Concept	Field theory and polynomials
Vector projection	Concept	Geometry
An orthonormal family is linearly independent	Proposition	Linear and multilinear algebra; matrix theory
Bayesian inference	Concept	Statistics
Sylow p-subgroup	Definition	Group theory and generalizations
Legendre's theorem on continued fractions	Theorem	Number theory
Galois group of a polynomial	Definition	Field theory and polynomials
Laplace transform of a derivative	Proposition	Integral transforms, operational calculus
Upper and lower Darboux sums	Concept	Real functions
Sum of a series	Definition	Sequences, series, summability
Lipschitz functions are uniformly continuous	Proposition	Real functions
Determinant of a triangular matrix	Proposition	Linear and multilinear algebra; matrix theory
Integral of 1/x	Proposition	Real functions
Scalar multiplication of matrices	Definition	Linear and multilinear algebra; matrix theory
Brahmagupta–Fibonacci identity	Proposition	Number theory
Logarithm of a product	Proposition	Special functions
Minkowski's theorem	Theorem	Number theory
Solving initial value problems with the Laplace transform	Concept	Integral transforms, operational calculus
Topologist's sine curve	Counterexample	General topology
Determinant of a matrix with two equal rows	Proposition	Linear and multilinear algebra; matrix theory
Rayleigh quotient	Definition	Linear and multilinear algebra; matrix theory
Homogeneous first-order equation	Definition	Ordinary differential equations
Action by left multiplication	Example	Group theory and generalizations
Complement of an open set is closed	Proposition	General topology
Alternating multilinear map	Concept	Linear and multilinear algebra; matrix theory
Young diagram	Definition	Combinatorics
Isolated zeros theorem	Theorem	Functions of a complex variable
Compactness and sequential compactness agree in metric spaces	Theorem	General topology
Lower central series	Concept	Group theory and generalizations
Continuous image of a compact set is compact	Proposition	General topology
Determinant via the Schur complement	Theorem	Linear and multilinear algebra; matrix theory
Upper and lower Darboux integrals	Concept	Real functions
Sum of binomial coefficients	Theorem	Combinatorics
Nondegenerate bilinear form	Definition	Linear and multilinear algebra; matrix theory
Subgroups of cyclic groups are cyclic	Theorem	Group theory and generalizations
Distributive law	Theorem	Mathematical logic and foundations
Reduced word	Concept	Group theory and generalizations
Fundamental solution of Pell's equation	Definition	Number theory
Classification of Pythagorean triples	Theorem	Number theory
The alternating group is generated by three-cycles	Proposition	Group theory and generalizations
Norm induced by an inner product	Definition	Functional analysis
Posterior probability	Concept	Statistics
Affine combination	Concept	Geometry
A polynomial over a field has at most as many roots as its degree	Theorem	Field theory and polynomials
One-sided limits of a monotone function exist	Theorem	Real functions
Fixed field	Definition	Field theory and polynomials
Determinant of a linear map is the determinant of its matrix	Proposition	Linear and multilinear algebra; matrix theory
Strong induction	Theorem	Mathematical logic and foundations