Nodes at W0, stub

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

Ideas 601–750 of 6044.

Name	Kind	Subject
Action on left cosets	Example	Group theory and generalizations
Equinumerous sets	Concept	Mathematical logic and foundations
Faithful action	Definition	Group theory and generalizations
Moment-generating function of the normal distribution	Proposition	Probability theory and stochastic processes
Curl-free vector field on a convex set is conservative	Theorem	Real functions
Open balls are open	Proposition	General topology
Level set	Concept	Real functions
Set bounded above	Definition	Order, lattices, ordered algebraic structures
Eigenvector	Definition	Linear and multilinear algebra; matrix theory
R[x] is an integral domain iff R is	Theorem	Commutative algebra
Legendre's three-square theorem	Theorem	Number theory
Ring isomorphism	Definition	Associative rings and algebras
Strict differentiability	Concept	Real functions
Markov property	Concept	Probability theory and stochastic processes
Arcsine	Definition	Special functions
Continuity via closed sets	Proposition	General topology
Orthogonal projection	Concept	Linear and multilinear algebra; matrix theory
Connected subsets of the real line are intervals	Theorem	General topology
Proof by contrapositive	Concept	General and overarching topics
Matrix determinant lemma	Theorem	Linear and multilinear algebra; matrix theory
Cycle type	Definition	Group theory and generalizations
Order of the Galois group of a Galois extension equals its degree	Theorem	Field theory and polynomials
Solutions for complex conjugate roots	Theorem	Ordinary differential equations
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
Tangent plane and normal vector of a surface	Definition	Differential geometry
Spanning set	Definition	Linear and multilinear algebra; matrix theory
Mertens' theorem on Cauchy products	Theorem	Sequences, series, summability
Square root of a positive semidefinite matrix	Concept	Linear and multilinear algebra; matrix theory
Coordinate vector	Definition	Linear and multilinear algebra; matrix theory
Fermat's little theorem in the form a^p = a	Corollary	Number theory
Uniformly Cauchy sequence of functions	Concept	Sequences, series, summability
Trees are bipartite	Proposition	Combinatorics
Polynomial of an endomorphism	Definition	Linear and multilinear algebra; matrix theory
Eigenvalue	Concept	Linear and multilinear algebra; matrix theory
Side-side-side congruence	Theorem	Geometry
Goursat's theorem	Theorem	Functions of a complex variable
Polar form	Theorem	Functions of a complex variable
Multiplication rule	Proposition	Probability theory and stochastic processes
Additive group of integers	Example	Group theory and generalizations
Z[√-5] is not a UFD	Counterexample	Number theory
Riemann's theorem on removable singularities	Theorem	Functions of a complex variable
Supremum	Definition	Order, lattices, ordered algebraic structures
Trajectory	Definition	Dynamical systems and ergodic theory
Pythagorean theorem in an inner product space	Theorem	Functional analysis
Antiderivative	Definition	Real functions
Characteristic polynomial of a linear recurrence	Definition	Difference and functional equations
Uniform limits commute with integration	Theorem	Sequences, series, summability
Power series converge uniformly on smaller discs inside the radius of convergence	Theorem	Functions of a complex variable
Ring of integers	Theorem	Commutative algebra
Minimal element	Concept	Order, lattices, ordered algebraic structures
Slopes of a convex function are increasing	Proposition	Real functions
Generalized pigeonhole principle	Theorem	Combinatorics
Least squares	Concept	Numerical analysis
Antiderivative	Concept	Real functions
Zero derivative on a connected open set implies constant	Theorem	Real functions
Characteristic polynomial of a linear map	Definition	Linear and multilinear algebra; matrix theory
Addition rule for two events	Proposition	Probability theory and stochastic processes
Order of the dihedral group	Proposition	Group theory and generalizations
Recurrence for Stirling numbers of the second kind	Theorem	Number theory
Laplace expansion along a row	Theorem	Linear and multilinear algebra; matrix theory
Separately continuous but not continuous function	Counterexample	Real functions
Density of the normal distribution	Concept	Probability theory and stochastic processes
Linear maps on finite-dimensional spaces are continuous	Theorem	Operator theory
Random variable with a density	Definition	Probability theory and stochastic processes
Rectifiable curve	Definition	Real functions
Determinant is the product of the eigenvalues	Theorem	Linear and multilinear algebra; matrix theory
Dual map	Definition	Linear and multilinear algebra; matrix theory
Associativity of addition	Theorem	Mathematical logic and foundations
Euler product formula	Theorem	Number theory
Eigenvalues of a self-adjoint operator are real	Theorem	Operator theory
Inclusion–exclusion for two sets	Theorem	Combinatorics
Recurrence for Stirling numbers of the first kind	Theorem	Number theory
Hyperbolic equilibrium point	Definition	Ordinary differential equations
Number of subsets of a finite set	Theorem	Combinatorics
Polynomial functions are continuous	Proposition	Real functions
Uncorrelated random variables that are not independent	Counterexample	Probability theory and stochastic processes
Contractive sequence	Concept	Sequences, series, summability
Reverse triangle inequality	Corollary	Real functions
The kernel is a normal subgroup	Proposition	Group theory and generalizations
Sequential compactness	Definition	General topology
Complex numbers as pairs of reals	Concept	Functions of a complex variable
Harmonic conjugate	Definition	Potential theory
Matrix–vector product	Definition	Linear and multilinear algebra; matrix theory
A finite field of order q is the splitting field of x^q - x	Theorem	Field theory and polynomials
Degrees along an Eulerian trail	Theorem	Combinatorics
Universal property of the free group	Theorem	Group theory and generalizations
Work done by a force field	Concept	Real functions
Arctangent	Concept	Special functions
Number of permutations	Theorem	Combinatorics
Zero of a holomorphic function	Definition	Functions of a complex variable
Polynomials in several variables	Definition	Commutative algebra
Classification of complex quadratic forms	Theorem	Number theory
exp(2 pi i/n) is a primitive root of unity	Proposition	Number theory
Frobenius automorphism of a finite field	Concept	Field theory and polynomials
Special orthogonal group	Object	Linear and multilinear algebra; matrix theory
Disc of convergence	Concept	Functions of a complex variable
Irreducible elements need not be prime	Counterexample	Commutative algebra
Division algorithm	Theorem	Number theory
Finite subgroups of the multiplicative group of a field are cyclic	Theorem	Field theory and polynomials
Impossibility of doubling the cube	Theorem	Field theory and polynomials
Absolute value is continuous but not differentiable at 0	Counterexample	Real functions
Bernoulli process	Concept	Probability theory and stochastic processes
Uniform convergence of derivatives allows term-by-term differentiation	Theorem	Sequences, series, summability
Exponential growth beats polynomial growth	Theorem	Real functions
Real sequence	Definition	Sequences, series, summability
Arccosine	Concept	Special functions
Improper multiple integral	Concept	Real functions
Integrating factor for a non-exact equation	Concept	Ordinary differential equations
First isomorphism theorem	Theorem	Group theory and generalizations
Linearity of the derivative	Proposition	Real functions
Derivative of a continuous linear map	Proposition	Real functions
Contractive sequence	Definition	Sequences, series, summability
Fibonacci recurrence	Fact	Number theory
Complex differentiability	Definition	Functions of a complex variable
Correspondence theorem for rings	Theorem	Associative rings and algebras
Conjugate elements	Definition	Group theory and generalizations
A set is closed iff it equals its closure	Corollary	General topology
Consecutive Fibonacci numbers are coprime	Theorem	Number theory
Order isomorphism	Concept	Order, lattices, ordered algebraic structures
Convergents of a continued fraction	Concept	Number theory
A continuous injective function on an interval is strictly monotone	Theorem	Real functions
Probability mass function	Concept	Probability theory and stochastic processes
Polynomial ring over a UFD is a UFD	Theorem	Commutative algebra
Power series in the complex plane	Concept	Functions of a complex variable
Zero is not a successor	Axiom	Mathematical logic and foundations
The exponential function is convex	Proposition	Real functions
Variance of a sum	Proposition	Probability theory and stochastic processes
Construction of the reals from Cauchy sequences	Concept	Real functions
Limits are unique in Hausdorff spaces	Proposition	General topology
Tangent vector of a curve	Definition	Differential geometry
Uniqueness of inverses	Proposition	Group theory and generalizations
Straightedge and compass construction	Concept	Geometry
Mean of the geometric distribution	Proposition	Probability theory and stochastic processes
Matrix of the adjoint is the conjugate transpose	Proposition	Linear and multilinear algebra; matrix theory
Right inverse	Definition	Mathematical logic and foundations
Finite extensions are algebraic	Proposition	Field theory and polynomials
Commutativity of addition	Theorem	Mathematical logic and foundations
Spectral theorem for Hermitian matrices	Theorem	Linear and multilinear algebra; matrix theory
Order of a permutation is the lcm of its cycle lengths	Proposition	Group theory and generalizations
Upper central series	Definition	Group theory and generalizations
Estimation lemma	Lemma	Functions of a complex variable
Cosets have the same cardinality as the subgroup	Proposition	Group theory and generalizations
K[x] is a Euclidean domain	Theorem	Commutative algebra
Universal property of the polynomial ring	Theorem	Commutative algebra