Every idea

Ideas 901–1050 of 7806.

Name	Kind	Subject
Picard's great theorem	Theorem	Functions of a complex variable
The sequence 1/n tends to zero	Example	Sequences, series, summability
Independence means the joint law is the product of the marginals	Proposition	Probability theory and stochastic processes
Partition of a set	Concept	Mathematical logic and foundations
Number of functions between finite sets	Theorem	Combinatorics
Cesàro mean	Concept	Sequences, series, summability
Number of distinct prime factors	Concept	Number theory
Liouville function	Definition	Number theory
Power series solution	Concept	Ordinary differential equations
Finite field	Definition	Field theory and polynomials
Normal extension	Concept	Field theory and polynomials
Differentiable on an open set	Definition	Real functions
Commutator subgroup	Definition	Group theory and generalizations
Permutation matrix	Concept	Linear and multilinear algebra; matrix theory
Topological embedding	Definition	General topology
Order of an element divides the order of the group	Corollary	Group theory and generalizations
Semisimple endomorphism	Concept	Linear and multilinear algebra; matrix theory
Content of a polynomial	Definition	Commutative algebra
Uniform convergence	Concept	Sequences, series, summability
Median	Definition	Probability theory and stochastic processes
Power series of cosine	Theorem	Special functions
Hall's marriage theorem	Theorem	Combinatorics
Cauchy–Binet formula	Theorem	Linear and multilinear algebra; matrix theory
Sine and cosine	Concept	Special functions
Euler's four-square identity	Proposition	Number theory
Explicit and implicit differential equations	Concept	Ordinary differential equations
Square-free integer	Concept	Number theory
An iterate of the Picard operator is a contraction	Lemma	Ordinary differential equations
Comparison of topologies	Definition	General topology
Integration by parts	Theorem	Real functions
Subfields of a finite field	Theorem	Field theory and polynomials
Steinitz exchange lemma	Lemma	Linear and multilinear algebra; matrix theory
Identically distributed random variables	Concept	Probability theory and stochastic processes
Alternating bilinear form	Definition	Linear and multilinear algebra; matrix theory
Eigenvalue method for linear systems	Concept	Ordinary differential equations
Tower of Hanoi	Example	General and overarching topics
One-sided limit	Definition	Real functions
Convergence of a sequence in a metric space	Concept	General topology
Hamiltonian graph	Definition	Combinatorics
Arithmetic function	Concept	Number theory
An injective endomorphism of a finite-dimensional space is surjective	Theorem	Linear and multilinear algebra; matrix theory
Real exponentiation	Concept	Real functions
Metrizable space	Concept	General topology
Geometric probability	Concept	Probability theory and stochastic processes
Euler's identity	Corollary	Special functions
Catalan numbers	Definition	Combinatorics
Binomial coefficient	Definition	Combinatorics
Lyapunov stability	Definition	Ordinary differential equations
Domain	Definition	Mathematical logic and foundations
Congruent triangles	Concept	Geometry
Mesh of a partition	Concept	Real functions
Minimal polynomial divides the characteristic polynomial	Corollary	Linear and multilinear algebra; matrix theory
Multiplication by a matrix as a linear map	Concept	Linear and multilinear algebra; matrix theory
Row equivalence	Definition	Linear and multilinear algebra; matrix theory
In a PID a nonzero element is irreducible iff it generates a maximal ideal	Theorem	Commutative algebra
Extended Euclidean algorithm	Concept	Number theory
Young diagram	Concept	Combinatorics
Unique paths in trees	Theorem	Combinatorics
Subnormal series	Definition	Group theory and generalizations
Divisibility	Definition	Number theory
Geometric solutions come from roots of the characteristic polynomial	Theorem	Difference and functional equations
Linearly independent set of the right size is a basis	Proposition	Linear and multilinear algebra; matrix theory
Ideal	Concept	Commutative algebra
Central moment	Concept	Probability theory and stochastic processes
Cramer's rule	Theorem	Linear and multilinear algebra; matrix theory
Riesz's lemma	Lemma	Functional analysis
Domain in the complex plane	Definition	Functions of a complex variable
Intermediate value theorem for connected spaces	Theorem	General topology
Fixed points of a p-group action	Lemma	Group theory and generalizations
Gauss–Jordan elimination	Concept	Linear and multilinear algebra; matrix theory
Combination	Concept	Combinatorics
Peano existence theorem	Theorem	Ordinary differential equations
Conditional probability	Concept	Probability theory and stochastic processes
Commutativity	Concept	General algebraic systems
Space of solutions of a linear recurrence	Concept	Difference and functional equations
Dirac measure	Definition	Measure and integration
Geometric multiplicity	Concept	Linear and multilinear algebra; matrix theory
Converse	Concept	Mathematical logic and foundations
Cross-ratio	Concept	Functions of a complex variable
Sequence tending to infinity	Definition	Sequences, series, summability
Discrete logarithm	Definition	Number theory
Power series of the complex logarithm	Proposition	Functions of a complex variable
Necessary and sufficient conditions	Concept	Mathematical logic and foundations
Heaviside step function	Object	Real functions
Area of a region as a line integral	Corollary	Real functions
Partition of a set	Definition	Mathematical logic and foundations
Cartesian product	Concept	Mathematical logic and foundations
Open sets characterised by neighbourhoods	Proposition	General topology
Transpose	Concept	Linear and multilinear algebra; matrix theory
Coordinates in an orthonormal basis	Proposition	Linear and multilinear algebra; matrix theory
Trace of a transpose	Proposition	Linear and multilinear algebra; matrix theory
Complex differentiability	Concept	Functions of a complex variable
Partial derivative	Concept	Real functions
Algebraic extension	Definition	Field theory and polynomials
Circuit	Concept	Combinatorics
Upper and lower Darboux integrals	Definition	Real functions
Complex numbers	Object	Functions of a complex variable
Epsilon-N definition of the limit of a sequence	Proposition	Sequences, series, summability
Second Sylow theorem	Theorem	Group theory and generalizations
Dihedral group	Definition	Group theory and generalizations
Transpose of a product	Proposition	Linear and multilinear algebra; matrix theory
Closed sets contain their limits	Proposition	General topology
Completeness of the space of bounded continuous functions	Theorem	General topology
The symmetric group S3	Example	Group theory and generalizations
Outer automorphism group	Definition	Group theory and generalizations
Euler's polyhedron formula	Theorem	Convex and discrete geometry
Method of moments	Concept	Statistics
Maximal ideal	Definition	Commutative algebra
Forest	Definition	Combinatorics
Sum of the totient over the divisors	Theorem	Number theory
Groups of order p squared are abelian	Theorem	Group theory and generalizations
Propositional logic	Concept	Mathematical logic and foundations
Metrizable space	Definition	General topology
Order of a differential equation	Definition	Ordinary differential equations
Ring homomorphisms from a field are injective	Proposition	Field theory and polynomials
Finite intersection of open sets is open	Proposition	General topology
Injective function	Concept	Mathematical logic and foundations
De Morgan's laws	Theorem	Mathematical logic and foundations
Mean of the normal distribution	Proposition	Probability theory and stochastic processes
Liouville's formula	Theorem	Ordinary differential equations
Prüfer sequence	Definition	Combinatorics
Bounded set	Concept	General topology
Removable singularity	Concept	Functions of a complex variable
Cancellation in congruences	Proposition	Number theory
The rationals form an ordered field	Theorem	Field theory and polynomials
Partial sum	Concept	Sequences, series, summability
Student's t-distribution	Concept	Probability theory and stochastic processes
Smooth non-analytic function	Counterexample	Real functions
Integral domain	Definition	Commutative algebra
Least common multiple	Definition	Number theory
Subbasis	Concept	General topology
Independent sigma-algebras	Definition	Probability theory and stochastic processes
Equivalent metrics	Concept	General topology
Scalar multiplication of matrices	Concept	Linear and multilinear algebra; matrix theory
Module over a ring	Definition	Associative rings and algebras
Singular value	Concept	Linear and multilinear algebra; matrix theory
Orthonormal family	Definition	Linear and multilinear algebra; matrix theory
Every walk contains a path	Proposition	Combinatorics
Local minimum	Concept	Real functions
Affine space	Concept	Geometry
Permuting rows multiplies the determinant by the sign	Proposition	Linear and multilinear algebra; matrix theory
Divisibility by 11	Proposition	Number theory
Intersection of closed sets is closed	Proposition	General topology
The number of Sylow subgroups is the index of the normaliser	Proposition	Group theory and generalizations
Product of compact sets is compact	Theorem	General topology
Linearisation at an equilibrium	Concept	Ordinary differential equations
Higher partial derivatives	Concept	Real functions
Determinant of a matrix exponential	Theorem	Linear and multilinear algebra; matrix theory
Isolated point	Concept	General topology
Open sets of a metric space	Proposition	General topology