Every idea

Ideas 2701–2850 of 7806.

Name	Kind	Subject
Upper bound	Concept	Order, lattices, ordered algebraic structures
Root of unity	Definition	Number theory
Biconditional	Concept	Mathematical logic and foundations
Confidence interval	Concept	Statistics
Midpoint	Concept	Geometry
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
Indeterminate form	Concept	Real functions
External direct sum	Concept	Linear and multilinear algebra; matrix theory
Centre of a group	Definition	Group theory and generalizations
Chain	Concept	Order, lattices, ordered algebraic structures
Hartman–Grobman theorem	Theorem	Dynamical systems and ergodic theory
Continuity in R^n	Definition	Real functions
Orthonormal basis	Concept	Linear and multilinear algebra; matrix theory
Correspondence theorem	Theorem	Group theory and generalizations
Generalised eigenvector	Definition	Linear and multilinear algebra; matrix theory
Derivative of tangent	Proposition	Special functions
Dirichlet convolution formula	Proposition	Number theory
Perfect number	Definition	Number theory
Path component	Definition	General topology
Multiplicative order	Definition	Number theory
Golden ratio	Object	Number theory
Hessian matrix	Definition	Real functions
Gradient theorem	Theorem	Real functions
Minor	Definition	Linear and multilinear algebra; matrix theory
Polynomial ring	Concept	Commutative algebra
Dihedral angle	Definition	Geometry
Multilinear map	Definition	Linear and multilinear algebra; matrix theory
Cross product	Definition	Linear and multilinear algebra; matrix theory
Order of a group	Definition	Group theory and generalizations
Countably infinite set	Definition	Mathematical logic and foundations
Product rule in several variables	Proposition	Real functions
Möbius transformation	Concept	Functions of a complex variable
Equivalence relation	Definition	Mathematical logic and foundations
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
Set	Definition	Mathematical logic and foundations
Continued fraction expansion of a real number	Definition	Number theory
Falling factorial	Concept	Combinatorics
Irreducibility of the cyclotomic polynomials over the rationals	Theorem	Number theory
Sign of a permutation	Definition	Group theory and generalizations
Stability of linear systems via eigenvalues	Theorem	Ordinary differential equations
General solution and particular solution	Concept	Ordinary differential equations
Edge bound for planar graphs	Theorem	Combinatorics
Prime number	Definition	Number theory
Erdős–Szekeres theorem	Theorem	Combinatorics
Bijective function	Definition	Mathematical logic and foundations
Primitive polynomial	Definition	Commutative algebra
A space is the direct sum of a subspace and its orthogonal complement	Theorem	Functional analysis
Existence of a prime divisor	Proposition	Number theory
Hypergeometric distribution	Definition	Probability theory and stochastic processes
Connected set	Concept	General topology
Change of basis for a bilinear form	Proposition	Linear and multilinear algebra; matrix theory
The Gaussian integers form a Euclidean domain	Theorem	Number theory
Refinement of a partition	Concept	Real functions
Branch of the logarithm	Definition	Special functions
Open map	Definition	General topology
Quadratic residue	Definition	Number theory
Principal value of the argument	Proposition	Functions of a complex variable
Even and odd permutations	Concept	Group theory and generalizations
Parallelepiped	Concept	Geometry
Bilinear form	Concept	Linear and multilinear algebra; matrix theory
Subgroups of the integers	Proposition	Group theory and generalizations
Characteristic subgroups are normal	Proposition	Group theory and generalizations
Convergents of a continued fraction	Definition	Number theory
Convergence in distribution	Concept	Probability theory and stochastic processes
First integral	Definition	Ordinary differential equations
Differentiation as a linear map	Example	Linear and multilinear algebra; matrix theory
Hurwitz's theorem	Theorem	Functions of a complex variable
Estimator	Concept	Statistics
The degree of a constructible number is a power of two	Theorem	Field theory and polynomials
Almost surely	Concept	Probability theory and stochastic processes
Adjoint of a linear map	Definition	Linear and multilinear algebra; matrix theory
Moments are derivatives of the moment-generating function at zero	Theorem	Probability theory and stochastic processes
C^1 functions are strictly differentiable	Proposition	Real functions
Density of the rationals	Theorem	Real functions
Sigma-algebra	Concept	Measure and integration
Almost sure convergence implies convergence in probability	Theorem	Probability theory and stochastic processes
Quotient space	Definition	Linear and multilinear algebra; matrix theory
Primitive element theorem	Theorem	Field theory and polynomials
Principal ideal	Concept	Commutative algebra
Linear equation with constant coefficients	Concept	Ordinary differential equations
Sample space	Concept	Probability theory and stochastic processes
Möbius transformations map circles and lines to circles and lines	Theorem	Functions of a complex variable
Dimension of a quotient space	Proposition	Linear and multilinear algebra; matrix theory
Acyclic graph	Concept	Combinatorics
Integral of 1/z around the unit circle	Example	Functions of a complex variable
Continuous map of topological spaces	Definition	General topology
Cauchy principal value	Concept	Real functions
Order of the alternating group	Proposition	Group theory and generalizations
Miller–Rabin primality test	Concept	Number theory
Normal convergence	Definition	Sequences, series, summability
Degree of a vertex	Definition	Combinatorics
Bertrand paradox	Example	Probability theory and stochastic processes
Normal core	Definition	Group theory and generalizations
Determinant is a coefficient of the characteristic polynomial	Proposition	Linear and multilinear algebra; matrix theory
Alternating group	Definition	Group theory and generalizations
Infinitely many primes congruent to 1 modulo n	Theorem	Number theory
Fundamental theorem of Galois theory	Theorem	Field theory and polynomials
Degree of a product	Proposition	Commutative algebra
Least element	Definition	Order, lattices, ordered algebraic structures
Subspace metric	Definition	General topology
Power series of arctangent	Theorem	Functions of a complex variable
Distributive lattice	Definition	Order, lattices, ordered algebraic structures
Predicate	Definition	Mathematical logic and foundations
Phase portrait	Concept	Ordinary differential equations
Limit superior	Concept	Sequences, series, summability
Frobenius endomorphism	Concept	Commutative algebra
Dirichlet function	Counterexample	Real functions
The cross product is perpendicular to its factors	Proposition	Linear and multilinear algebra; matrix theory
Clairaut's equation	Example	Ordinary differential equations
Augmented matrix	Concept	Linear and multilinear algebra; matrix theory
First Borel–Cantelli lemma	Lemma	Probability theory and stochastic processes
Cauchy–Riemann equations	Theorem	Functions of a complex variable
Circle integral	Definition	Functions of a complex variable
Tangent line to a circle	Concept	Geometry
Integration in polar coordinates	Theorem	Real functions
The characteristic function determines the distribution	Theorem	Probability theory and stochastic processes
Existence of finite fields of every prime power order	Theorem	Field theory and polynomials
Bernoulli equation	Concept	Ordinary differential equations
Carmichael number	Definition	Number theory
Axiom of extensionality	Axiom	Mathematical logic and foundations
The successor function is injective	Axiom	Mathematical logic and foundations
Dirac's theorem on Hamiltonian cycles	Theorem	Combinatorics
C^k function characterised by continuous derivatives	Proposition	Real functions
Convex hull	Definition	Convex and discrete geometry
Orientable surface	Concept	Differential geometry
Product of the gcd and the lcm	Proposition	Number theory
Remainder theorem	Theorem	Commutative algebra
Affine space	Definition	Geometry
p-metric on R^n	Example	Functional analysis
Big O notation	Concept	Approximations and expansions
Derangement	Definition	Combinatorics
Arc length	Concept	Real functions
Reduction of a higher-order equation to a first-order system	Proposition	Ordinary differential equations
Function composition	Concept	Mathematical logic and foundations
Conditional independence	Concept	Probability theory and stochastic processes
Third isomorphism theorem	Theorem	Group theory and generalizations
Term-by-term differentiation	Theorem	Sequences, series, summability
Interval	Definition	Real functions
Cylindrical coordinates	Concept	Geometry
Bounded derivative on a convex set implies Lipschitz	Corollary	Real functions
Bell numbers	Concept	Number theory
Orthogonal group	Object	Linear and multilinear algebra; matrix theory
Minimum degree	Definition	Combinatorics
Lipschitz map	Definition	Real functions
Set-builder notation	Concept	Mathematical logic and foundations
Powers of a diagonalisable matrix	Concept	Linear and multilinear algebra; matrix theory