Every idea

Ideas 2551–2700 of 7806.

Name	Kind	Subject
Upper and lower Darboux sums	Definition	Real functions
Recurrence for derangements	Theorem	Combinatorics
Residue class	Definition	Number theory
Semisimple endomorphism	Definition	Linear and multilinear algebra; matrix theory
The reals form an ordered field	Theorem	Field theory and polynomials
Homeomorphism	Concept	General topology
The group of units of Z/pZ is cyclic	Theorem	Number theory
Frattini argument	Lemma	Group theory and generalizations
Partial order	Concept	Order, lattices, ordered algebraic structures
Distance in a graph	Concept	Combinatorics
Integral domain	Concept	Commutative algebra
Homothety	Definition	Geometry
Inner product space	Concept	Linear and multilinear algebra; matrix theory
Dimension of a subspace	Proposition	Linear and multilinear algebra; matrix theory
Simply connected domain	Concept	Algebraic topology
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
Tangent–secant theorem	Theorem	Geometry
Picard–Lindelöf hypotheses	Concept	Ordinary differential equations
Convergent sequences are Cauchy	Proposition	Sequences, series, summability
Presentation of a group	Definition	Group theory and generalizations
Cauchy sequence	Definition	Sequences, series, summability
Fermat number	Definition	Number theory
Coefficient of a power series	Concept	Commutative algebra
Continuity of the sum of a uniformly convergent series of functions	Corollary	Sequences, series, summability
Fubini's theorem	Theorem	Real functions
Abelian groups are solvable	Proposition	Group theory and generalizations
Content of a polynomial	Concept	Commutative algebra
Connected set	Definition	General topology
T0 space	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
Almost surely	Definition	Probability theory and stochastic processes
Monoid	Definition	Group theory and generalizations
Directed graph	Definition	Combinatorics
Translation	Definition	Geometry
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
Subsequence	Definition	Sequences, series, summability
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
Linear Diophantine equation	Concept	Number theory
Dyck word	Definition	Computer science
Adjoint of a linear map	Concept	Linear and multilinear algebra; matrix theory
One-sided derivative	Concept	Real functions
Unitary group	Object	Linear and multilinear algebra; matrix theory
Limit of a sum of sequences	Proposition	Sequences, series, summability
Bernoulli number	Definition	Number theory
Focus of a conic	Concept	Geometry
Quadratic form	Concept	Linear and multilinear algebra; matrix theory
Bessel's inequality	Theorem	Functional analysis
Cluster point of a sequence	Definition	Sequences, series, summability
Cyclic quadrilateral	Concept	Geometry
Indicator function	Concept	Mathematical logic and foundations
Boolean ring	Concept	Order, lattices, ordered algebraic structures
Ordinal number	Definition	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
Chi-squared distribution	Definition	Probability theory and stochastic processes
Composition factors	Definition	Group theory and generalizations
Cauchy–Schwarz inequality	Theorem	Linear and multilinear algebra; matrix theory
Subgroup generated by a subset	Definition	Group theory and generalizations
Stabiliser	Definition	Group theory and generalizations
Incircle	Definition	Geometry
Submodule	Definition	Associative rings and algebras
Torsion subgroup	Definition	Group theory and generalizations
Projection	Definition	Linear and multilinear algebra; matrix theory
Picard iteration	Concept	Ordinary differential equations
Limit of the cumulative distribution function at infinity	Proposition	Probability theory and stochastic processes
Linear map	Definition	Linear and multilinear algebra; matrix theory
Symmetric group	Definition	Group theory and generalizations
Totally disconnected space	Concept	General topology
Polar coordinates	Definition	Geometry
Circumcircle	Definition	Geometry
Complement	Concept	Mathematical logic and foundations
LU decomposition	Concept	Linear and multilinear algebra; matrix theory
Slope field	Definition	Ordinary differential equations
Logarithm is the inverse of the exponential	Theorem	Special functions
Sum of subspaces	Definition	Linear and multilinear algebra; matrix theory
Exponential function	Definition	Special functions
Inner automorphism	Concept	Group theory and generalizations
Proper metric space	Concept	General topology
Homogeneous first-order equation	Concept	Ordinary differential equations
Complex power	Concept	Special functions
Complement graph	Definition	Combinatorics
Damped harmonic oscillator	Example	Mechanics of particles and systems
Positive definite quadratic form	Concept	Linear and multilinear algebra; matrix theory
Subgroup generated by a subset	Concept	Group theory and generalizations
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
Identity element	Definition	General algebraic systems
Prime-counting function	Concept	Number theory
Wedderburn's little theorem	Theorem	Field theory and polynomials
Fixed points of an action	Concept	Group theory and generalizations
Linear form	Definition	Linear and multilinear algebra; matrix theory
Focus of a conic	Definition	Geometry
Cauchy product	Concept	Sequences, series, summability
Gaussian prime	Concept	Number theory
Converse	Definition	Mathematical logic and foundations
Spherical coordinates	Definition	Geometry
Orthonormal family	Concept	Linear and multilinear algebra; matrix theory
Probability theory	Concept	Probability theory and stochastic processes
Cartesian coordinate system	Concept	Geometry
Jensen's inequality	Theorem	Real functions
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
Completely multiplicative function	Concept	Number theory
Preorder	Definition	Order, lattices, ordered algebraic structures
Chain rule	Theorem	Real functions
Structure theorem for finitely generated abelian groups	Theorem	Group theory and generalizations
Lucas's theorem	Theorem	Number theory
Big O notation	Definition	Approximations and expansions
Law of excluded middle	Theorem	Mathematical logic and foundations
Separable polynomial	Concept	Field theory and polynomials
A nontrivial finite p-group has nontrivial centre	Theorem	Group theory and generalizations
Interior	Concept	General topology
Principal ideal domain	Definition	Commutative algebra
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
Hausdorff space	Concept	General topology
Variation of constants formula for linear systems	Theorem	Ordinary differential equations
Image of a homomorphism	Concept	Group theory and generalizations
Kernel of a linear map	Concept	Linear and multilinear algebra; matrix theory
Surface area	Concept	Measure and integration
Smallest prime factor	Definition	Number theory
Discrete topology	Example	General topology
Continuous linear map	Definition	Operator theory
Abel's theorem	Theorem	Sequences, series, summability
Convergent sequences are bounded	Proposition	Sequences, series, summability
Inverse of a product	Proposition	Linear and multilinear algebra; matrix theory
Spanning tree	Concept	Combinatorics
Dot product	Concept	Linear and multilinear algebra; matrix theory