Nodes at W0, stub

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

Ideas 1351–1500 of 6044.

Name	Kind	Subject
Continued fraction expansion of a real number	Definition	Number theory
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
A space is the direct sum of a subspace and its orthogonal complement	Theorem	Functional analysis
Existence of a prime divisor	Proposition	Number theory
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
Principal value of the argument	Proposition	Functions of a complex variable
Even and odd permutations	Concept	Group theory and generalizations
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
First integral	Definition	Ordinary differential equations
Differentiation as a linear map	Example	Linear and multilinear algebra; matrix theory
The degree of a constructible number is a power of two	Theorem	Field theory and polynomials
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
Almost sure convergence implies convergence in probability	Theorem	Probability theory and stochastic processes
Linear equation with constant coefficients	Concept	Ordinary differential equations
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
Integral of 1/z around the unit circle	Example	Functions of a complex variable
Continuous map of topological spaces	Definition	General topology
Order of the alternating group	Proposition	Group theory and generalizations
Normal core	Definition	Group theory and generalizations
Determinant is a coefficient of the characteristic polynomial	Proposition	Linear and multilinear algebra; matrix theory
Infinitely many primes congruent to 1 modulo n	Theorem	Number theory
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
Limit superior	Concept	Sequences, series, summability
Dirichlet function	Counterexample	Real functions
The cross product is perpendicular to its factors	Proposition	Linear and multilinear algebra; matrix theory
First Borel–Cantelli lemma	Lemma	Probability theory and stochastic processes
Circle integral	Definition	Functions of a complex variable
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
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
Product of the gcd and the lcm	Proposition	Number theory
p-metric on R^n	Example	Functional analysis
Reduction of a higher-order equation to a first-order system	Proposition	Ordinary differential equations
Conditional independence	Concept	Probability theory and stochastic processes
Third isomorphism theorem	Theorem	Group theory and generalizations
Term-by-term differentiation	Theorem	Sequences, series, summability
Bounded derivative on a convex set implies Lipschitz	Corollary	Real functions
Minimum degree	Definition	Combinatorics
Set-builder notation	Concept	Mathematical logic and foundations
Powers of a diagonalisable matrix	Concept	Linear and multilinear algebra; matrix theory
Prime subfield	Concept	Field theory and polynomials
Partial derivatives do not imply differentiability	Counterexample	Real functions
Circumcentre	Definition	Geometry
Congruence modulo n	Definition	Number theory
An algebraic extension of an algebraic extension is algebraic	Theorem	Field theory and polynomials
Strictly monotone function	Definition	Real functions
Orthogonal vectors	Definition	Linear and multilinear algebra; matrix theory
Law of a random variable	Definition	Probability theory and stochastic processes
Real exponentiation	Definition	Real functions
Equivalent metrics	Definition	General topology
Symmetric bilinear form associated with a quadratic form	Definition	Linear and multilinear algebra; matrix theory
Integration over a non-rectangular region	Concept	Real functions
Product of a subgroup and a normal subgroup is a subgroup	Proposition	Group theory and generalizations
Characteristic polynomial does not depend on the basis	Proposition	Linear and multilinear algebra; matrix theory
Surjective iff it has a right inverse	Proposition	Mathematical logic and foundations
Row rank equals column rank	Theorem	Linear and multilinear algebra; matrix theory
The sequence r^n tends to infinity for r > 1	Example	Sequences, series, summability
Variance of a sum of independent random variables	Theorem	Probability theory and stochastic processes
Sign of a cycle	Proposition	Group theory and generalizations
Derivative of cosine	Theorem	Special functions
Intersection of subspaces	Proposition	Linear and multilinear algebra; matrix theory
Plane	Concept	Geometry
Continuous real function on a compact set attains its bounds	Theorem	General topology
Separable equation	Definition	Ordinary differential equations
Vacuous truth	Concept	Mathematical logic and foundations
Fibonacci numbers as sums of binomial coefficients	Theorem	Number theory
Mean squared error	Definition	Statistics
Subgroups of index two are normal	Proposition	Group theory and generalizations
Biconditional	Definition	Mathematical logic and foundations
Regular curve	Concept	Differential geometry
Square root function	Definition	Real functions
Logarithm of a power	Corollary	Special functions
Determinant of a family of vectors in a basis	Definition	Linear and multilinear algebra; matrix theory
First Sylow theorem	Theorem	Group theory and generalizations
Dirichlet's test	Theorem	Sequences, series, summability
Power series in the complex plane	Definition	Functions of a complex variable
Multiplicativity of the Möbius function	Proposition	Number theory
Kummer's theorem	Theorem	Number theory
Internal direct product	Concept	Group theory and generalizations
Volume of a box	Proposition	Measure and integration
Every polynomial has a root in some extension field	Theorem	Field theory and polynomials
Continuous map	Concept	General topology
Improper integral of x^p on an unbounded interval	Example	Sequences, series, summability
Product of continuous functions is continuous	Proposition	Real functions
Continuity is equivalent to sequential continuity in metric spaces	Theorem	General topology
Conditional variance	Concept	Probability theory and stochastic processes
Subsequences of a convergent sequence converge to the same limit	Proposition	Sequences, series, summability
Finite-dimensional spaces are isomorphic iff they have equal dimension	Theorem	Linear and multilinear algebra; matrix theory
Homogeneous linear system with constant coefficients	Definition	Ordinary differential equations
Walk	Definition	Combinatorics
De Morgan's laws for sets	Theorem	Mathematical logic and foundations
Size of a conjugacy class is the index of the centraliser	Proposition	Group theory and generalizations
Limit of a function of several variables	Definition	Real functions
Smallest prime factor	Concept	Number theory
If 2^n + 1 is prime then n is a power of 2	Proposition	Number theory
Polynomials of degree two or three are irreducible iff they have no roots	Proposition	Field theory and polynomials
Frobenius automorphism of a finite field	Definition	Field theory and polynomials
Space of linear maps	Definition	Linear and multilinear algebra; matrix theory
Prime subfield	Definition	Field theory and polynomials
Sequence tending to infinity	Concept	Sequences, series, summability
Combinations with repetition	Concept	Combinatorics
Isometric isomorphism	Definition	General topology
Indicator function	Definition	Mathematical logic and foundations
A tree on n vertices has n − 1 edges	Theorem	Combinatorics
Cancellation laws	Proposition	Group theory and generalizations
Minimal polynomial divides every annihilating polynomial	Proposition	Linear and multilinear algebra; matrix theory
Order of a power	Proposition	Group theory and generalizations
Gradient is orthogonal to level sets	Proposition	Real functions
Bézout's identity in a Euclidean domain	Theorem	Commutative algebra
Row echelon form	Concept	Linear and multilinear algebra; matrix theory
Compact closed unit ball implies finite dimension	Theorem	Functional analysis
Continuous functions on a closed bounded interval are uniformly continuous	Theorem	Real functions
Euler's formula for planar graphs	Theorem	Combinatorics
Rearrangement of a series	Concept	Sequences, series, summability
Uniform convergence on a set	Concept	Sequences, series, summability
Linear approximation	Concept	Real functions
Cofactor	Definition	Linear and multilinear algebra; matrix theory
Line integral as an integral over the parameter interval	Theorem	Real functions
Complete subspaces are closed	Proposition	General topology
Irrationality of e	Theorem	Number theory
Trail	Concept	Combinatorics
Addition of natural numbers	Definition	Mathematical logic and foundations
Law of total probability for an event and its complement	Corollary	Probability theory and stochastic processes
Epsilon-delta definition of continuity	Proposition	Real functions
Fermat pseudoprime	Concept	Number theory
Chinese remainder theorem for rings	Theorem	Commutative algebra
Time translation of solutions of an autonomous system	Proposition	Ordinary differential equations
Congruence modulo n	Concept	Number theory
Sine and cosine	Definition	Special functions
Subgraph	Concept	Combinatorics