Every idea

Ideas 1051–1200 of 7806.

Name	Kind	Subject
Convergence in mean	Concept	Probability theory and stochastic processes
Uniform continuity on a set	Definition	Real functions
The reals are Archimedean	Theorem	Real functions
Pseudometric space	Concept	General topology
Boolean function	Definition	Order, lattices, ordered algebraic structures
Differentiable function	Definition	Real functions
Linear equation with constant coefficients	Definition	Ordinary differential equations
Derivative gives the directional derivatives	Proposition	Real functions
System of linear differential equations	Definition	Ordinary differential equations
Metric topology	Definition	General topology
Archimedean property	Proposition	Field theory and polynomials
Baire category theorem	Theorem	General topology
Tower law	Theorem	Field theory and polynomials
Monotone function	Concept	Order, lattices, ordered algebraic structures
Complex sine and cosine	Definition	Special functions
Bounded sequence	Concept	Sequences, series, summability
x^2 is not uniformly continuous on the real line	Counterexample	Real functions
Chain rule for a composition with a curve	Corollary	Real functions
Complete ordered field	Concept	Field theory and polynomials
Chi-squared distribution	Concept	Probability theory and stochastic processes
Schröder–Bernstein theorem	Theorem	Mathematical logic and foundations
Periodic orbit	Concept	Dynamical systems and ergodic theory
Kernel of a ring homomorphism	Definition	Associative rings and algebras
Least element	Concept	Order, lattices, ordered algebraic structures
Limit cycle	Concept	Ordinary differential equations
Almost sure convergence	Concept	Probability theory and stochastic processes
Gradient	Concept	Real functions
Finite-dimensional normed spaces are complete	Theorem	Functional analysis
Dirac measure	Concept	Measure and integration
Invariant subspace	Concept	Linear and multilinear algebra; matrix theory
Metrizable spaces are normal	Proposition	General topology
Formal derivative	Definition	Commutative algebra
Jacobi symbol	Concept	Number theory
Strictly convex function	Concept	Real functions
Prime factorization	Definition	Number theory
Pell's equation	Definition	Number theory
Convergent series	Concept	Sequences, series, summability
Collinear points	Concept	Geometry
sin(1/x) has no limit at 0	Counterexample	Real functions
If G modulo its centre is cyclic then G is abelian	Proposition	Group theory and generalizations
Vertex cover	Concept	Combinatorics
Generalised eigenspace	Concept	Linear and multilinear algebra; matrix theory
Multiplication by a matrix as a linear map	Definition	Linear and multilinear algebra; matrix theory
Annulus	Definition	Functions of a complex variable
Normal space	Definition	General topology
Independent and identically distributed random variables	Definition	Probability theory and stochastic processes
Step function	Concept	Real functions
Successor function	Concept	Mathematical logic and foundations
Classical definition of probability	Definition	Probability theory and stochastic processes
Stokes' theorem	Theorem	Real functions
Gram matrices are positive semidefinite	Proposition	Linear and multilinear algebra; matrix theory
Cauchy product of absolutely convergent series	Theorem	Sequences, series, summability
Circle integral	Concept	Functions of a complex variable
Multiplicative function	Definition	Number theory
Nullity	Concept	Linear and multilinear algebra; matrix theory
Second isomorphism theorem for vector spaces	Theorem	Linear and multilinear algebra; matrix theory
Edge set	Concept	Combinatorics
The symmetric group is generated by transpositions	Proposition	Group theory and generalizations
Abelianisation	Concept	Group theory and generalizations
Differentiation under the integral sign	Theorem	Real functions
Pairwise independent events that are not mutually independent	Counterexample	Probability theory and stochastic processes
Unitary matrix	Concept	Linear and multilinear algebra; matrix theory
Continuous uniform distribution	Concept	Probability theory and stochastic processes
Simplicity of the alternating group	Theorem	Group theory and generalizations
Power sum symmetric polynomials	Definition	Combinatorics
Consistent estimator	Concept	Statistics
The Möbius function is the inverse of the constant function 1	Theorem	Number theory
Block matrix	Concept	Linear and multilinear algebra; matrix theory
Commutator subgroup	Concept	Group theory and generalizations
Annihilator of a subspace	Concept	Linear and multilinear algebra; matrix theory
Mathematical induction	Concept	Mathematical logic and foundations
Ceiling function	Definition	Real functions
Normaliser	Definition	Group theory and generalizations
Periodic function	Concept	Real functions
Back substitution	Concept	Linear and multilinear algebra; matrix theory
Boundedness theorem	Theorem	Real functions
The nth root of n tends to 1	Example	Sequences, series, summability
R/P is an integral domain iff P is prime	Theorem	Commutative algebra
Totient of a prime power	Proposition	Number theory
Lipschitz condition	Concept	Real functions
K[x]/(f) is a field iff f is irreducible	Theorem	Field theory and polynomials
Marginal distribution	Definition	Statistics
Completeness axiom	Axiom	Real functions
Symmetric bilinear form	Concept	Linear and multilinear algebra; matrix theory
Eigenspace	Definition	Linear and multilinear algebra; matrix theory
Stabiliser	Concept	Group theory and generalizations
Product metric	Concept	General topology
Convergent sequence	Definition	Sequences, series, summability
Dual map	Concept	Linear and multilinear algebra; matrix theory
Action on left cosets	Example	Group theory and generalizations
Equinumerous sets	Concept	Mathematical logic and foundations
Faithful action	Definition	Group theory and generalizations
Ring	Concept	Associative rings and algebras
Complement	Definition	Mathematical logic and foundations
Moment-generating function of the normal distribution	Proposition	Probability theory and stochastic processes
Cauchy product	Definition	Sequences, series, summability
Curl-free vector field on a convex set is conservative	Theorem	Real functions
Open balls are open	Proposition	General topology
Gaussian integer	Definition	Number theory
Level set	Concept	Real functions
Möbius transformation	Definition	Functions of a complex variable
Conjunctive normal form	Concept	Mathematical logic and foundations
Quantile function	Definition	Probability theory and stochastic processes
Independent sigma-algebras	Concept	Probability theory and stochastic processes
Set bounded above	Definition	Order, lattices, ordered algebraic structures
Eigenvector	Definition	Linear and multilinear algebra; matrix theory
Edge colouring	Concept	Combinatorics
R[x] is an integral domain iff R is	Theorem	Commutative algebra
Chromatic polynomial	Concept	Combinatorics
Legendre's three-square theorem	Theorem	Number theory
Lexicographic order	Concept	Order, lattices, ordered algebraic structures
Ring isomorphism	Definition	Associative rings and algebras
Strict differentiability	Concept	Real functions
Markov property	Concept	Probability theory and stochastic processes
Gamma distribution	Concept	Probability theory and stochastic processes
Cyclic group	Definition	Group theory and generalizations
Order of a group	Concept	Group theory and generalizations
Essential singularity	Concept	Functions of a complex variable
Universal quantifier	Definition	Mathematical logic and foundations
Arcsine	Definition	Special functions
Lattice of subgroups	Concept	Group theory and generalizations
Continuity via closed sets	Proposition	General topology
Orthogonal projection	Concept	Linear and multilinear algebra; matrix theory
Linear isomorphism	Concept	Linear and multilinear algebra; matrix theory
Cofinite topology	Example	General topology
Mathematical proof	Concept	General and overarching topics
Cauchy condensation test	Theorem	Sequences, series, summability
Rotation matrix	Example	Linear and multilinear algebra; matrix theory
Connected subsets of the real line are intervals	Theorem	General topology
Bridge	Concept	Combinatorics
Mean value theorem	Theorem	Real functions
Proof by contrapositive	Concept	General and overarching topics
Finite set	Definition	Mathematical logic and foundations
Matrix determinant lemma	Theorem	Linear and multilinear algebra; matrix theory
Power set	Definition	Mathematical logic and foundations
Cycle type	Definition	Group theory and generalizations
Pivot	Definition	Linear and multilinear algebra; matrix theory
Order of the Galois group of a Galois extension equals its degree	Theorem	Field theory and polynomials
Banach space	Definition	Functional analysis
Monic polynomial	Definition	Commutative algebra
Smooth function	Definition	Real functions
Solutions for complex conjugate roots	Theorem	Ordinary differential equations
Tensor product of vector spaces	Concept	Linear and multilinear algebra; matrix theory
Global existence for globally Lipschitz vector fields	Theorem	Ordinary differential equations
Weak law of large numbers	Theorem	Probability theory and stochastic processes
Number of k-element subsets	Theorem	Combinatorics
Path independence of line integrals	Theorem	Real functions
Infinite limit	Concept	Real functions
Limit along different paths	Concept	Real functions
A linear map is injective iff its kernel is trivial	Proposition	Linear and multilinear algebra; matrix theory