Nodes at W0, stub

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

Ideas 1–150 of 12399.

Name	Kind	Subject
The integers are a Euclidean domain	Theorem	Number theory
Sequential characterization of limits	Theorem	Real functions
Mutual independence of events	Concept	Probability theory and stochastic processes
Power series are differentiable inside the radius of convergence	Theorem	Functions of a complex variable
A function with zero derivative is constant	Corollary	Real functions
Closure is the set of limits of sequences	Proposition	General topology
Power set Boolean algebra	Example	Order, lattices, ordered algebraic structures
Sylow p-subgroup	Concept	Group theory and generalizations
A differentiable function is convex iff its derivative is increasing	Theorem	Real functions
Taylor's theorem with the Cauchy remainder	Theorem	Approximations and expansions
Row equivalence	Concept	Linear and multilinear algebra; matrix theory
The characteristic of an integral domain is zero or prime	Theorem	Commutative algebra
Dimension of the dual space	Proposition	Linear and multilinear algebra; matrix theory
Linear map of a matrix	Definition	Linear and multilinear algebra; matrix theory
Scaling a row scales the determinant	Proposition	Linear and multilinear algebra; matrix theory
Sum of divisors	Definition	Number theory
Stars and bars	Theorem	Combinatorics
One-sided limit	Concept	Real functions
Composition of linear maps	Concept	Linear and multilinear algebra; matrix theory
Picard–Lindelöf theorem in integral form	Theorem	Ordinary differential equations
Addition formula for Fibonacci numbers	Theorem	Number theory
The logarithm grows slower than any power	Theorem	Real functions
Laws of exponents in a group	Proposition	Group theory and generalizations
−1 is a square modulo p if and only if p is not 3 modulo 4	Corollary	Number theory
Root of a polynomial	Definition	Commutative algebra
Orbit	Definition	Group theory and generalizations
Closed map	Concept	General topology
Congruence is compatible with addition	Proposition	Number theory
Zero of a holomorphic function	Concept	Functions of a complex variable
Norm of a Gaussian integer	Definition	Number theory
Divisibility rule	Concept	Number theory
Nullity	Definition	Linear and multilinear algebra; matrix theory
Non-uniqueness for a non-Lipschitz equation	Counterexample	Ordinary differential equations
Modulus of the conjugate	Proposition	Functions of a complex variable
Independent and identically distributed random variables	Concept	Probability theory and stochastic processes
Every vector space has a basis	Theorem	Linear and multilinear algebra; matrix theory
Change of variables in multiple integrals	Theorem	Real functions
Prior probability	Concept	Statistics
Complex sine and cosine	Concept	Special functions
Primitive element of a finite field	Concept	Field theory and polynomials
Compact set	Definition	General topology
Arc length parametrisation	Definition	Differential geometry
Derivative of sine	Theorem	Special functions
Divergence of the sum of the reciprocals of the primes	Theorem	Number theory
Asymptotic equivalence	Definition	Approximations and expansions
Little o notation	Concept	Approximations and expansions
Picard operator	Definition	Ordinary differential equations
A finite group is nilpotent iff it is the product of its Sylow subgroups	Theorem	Group theory and generalizations
Volume of a ball in R^n	Theorem	Measure and integration
Arcsine	Concept	Special functions
Additivity of line integrals under concatenation	Proposition	Real functions
Topological embedding	Concept	General topology
Uniqueness of finite fields of a given order	Theorem	Field theory and polynomials
Recurrence for Bell numbers	Theorem	Number theory
Image of a homomorphism	Definition	Group theory and generalizations
Strictly monotone function	Concept	Real functions
A convex function on an open interval is continuous	Theorem	Real functions
Jordan–Chevalley decomposition	Theorem	Linear and multilinear algebra; matrix theory
Evaluation homomorphism	Definition	Commutative algebra
1 + x is at most exp x	Proposition	Special functions
Reduction formula	Concept	Real functions
Differentiable function of several variables	Definition	Real functions
exp z = 1 iff z is an integer multiple of 2πi	Proposition	Special functions
Existence of splitting fields	Theorem	Field theory and polynomials
Strict differentiability	Definition	Real functions
Chernoff bound	Theorem	Probability theory and stochastic processes
Integral equation form of an initial value problem	Proposition	Ordinary differential equations
Glide reflection	Concept	Geometry
Leibniz formula for determinants	Theorem	Linear and multilinear algebra; matrix theory
Riemann's criterion for integrability	Theorem	Real functions
Dyck words are counted by Catalan numbers	Theorem	Combinatorics
Finite-dimensional vector space	Definition	Linear and multilinear algebra; matrix theory
Residue at a simple pole	Proposition	Functions of a complex variable
Derivative of the complex exponential	Proposition	Special functions
Root of a polynomial	Concept	Commutative algebra
Integral test	Theorem	Sequences, series, summability
Maximal solution	Definition	Ordinary differential equations
Weierstrass function	Counterexample	Real functions
First derivative test	Proposition	Real functions
cos pi = -1	Proposition	Special functions
Distance from a point to a line	Proposition	Geometry
Preimage of a set	Concept	Mathematical logic and foundations
The complex numbers cannot be ordered	Theorem	Field theory and polynomials
Periodic orbit	Definition	Ordinary differential equations
Normality via left and right cosets	Proposition	Group theory and generalizations
Law of a random variable	Concept	Probability theory and stochastic processes
Determinant of a scalar multiple	Proposition	Linear and multilinear algebra; matrix theory
Extensions of solvable groups are solvable	Proposition	Group theory and generalizations
Composition of injections is injective	Proposition	Mathematical logic and foundations
Periodic continued fraction	Concept	Number theory
Order of cardinals	Definition	Mathematical logic and foundations
Equivalence classes form a partition	Theorem	Mathematical logic and foundations
Maximal solution	Concept	Ordinary differential equations
Triangle inequality for a metric	Axiom	General topology
Integers modulo n	Definition	Number theory
Nondegenerate bilinear form	Concept	Linear and multilinear algebra; matrix theory
Function with unequal mixed partial derivatives	Counterexample	Real functions
Similar triangles	Definition	Geometry
sin x / x tends to 1	Proposition	Special functions
Sum of the first n natural numbers	Theorem	Combinatorics
A graph is bipartite iff it has no odd cycle	Theorem	Combinatorics
Definite and indefinite quadratic forms	Concept	Linear and multilinear algebra; matrix theory
Elementary matrix	Concept	Linear and multilinear algebra; matrix theory
Composition of relations	Definition	Mathematical logic and foundations
Neighbourhood	Definition	Combinatorics
Hyperbolic equilibrium point	Concept	Dynamical systems and ergodic theory
Orthogonal family for a bilinear form	Concept	Linear and multilinear algebra; matrix theory
Bijective iff it has a two-sided inverse	Proposition	Mathematical logic and foundations
Quadratic integer	Definition	Number theory
Uniqueness of the algebraic closure	Theorem	Field theory and polynomials
Cantor set is closed	Proposition	General topology
Arguments add under multiplication	Theorem	Functions of a complex variable
Legendre's formula	Theorem	Number theory
Identically distributed random variables	Definition	Probability theory and stochastic processes
Uniformly Cauchy sequence of functions	Definition	Sequences, series, summability
Limit at infinity	Concept	Real functions
Adding a multiple of one row to another preserves the determinant	Proposition	Linear and multilinear algebra; matrix theory
Law of the unconscious statistician	Theorem	Probability theory and stochastic processes
Euler's theorem on Eulerian circuits	Theorem	Combinatorics
Existence of prime factorization	Theorem	Number theory
Darboux and Riemann integrals agree	Theorem	Real functions
Order of cardinals	Concept	Mathematical logic and foundations
Euclidean algorithm in a Euclidean domain	Concept	Commutative algebra
Left inverse	Definition	Mathematical logic and foundations
Uniqueness of solutions for Lipschitz vector fields	Theorem	Ordinary differential equations
First integral	Concept	Ordinary differential equations
A function with nonnegative derivative is increasing	Corollary	Real functions
Uniformly continuous functions map Cauchy sequences to Cauchy sequences	Proposition	Real functions
Flux through a surface	Concept	Real functions
Density of the normal distribution	Definition	Probability theory and stochastic processes
Derivative function	Definition	Real functions
Quotients of solvable groups are solvable	Proposition	Group theory and generalizations
Associate elements	Concept	Commutative algebra
Angle addition formulas	Theorem	Special functions
Holomorphic functions on a disc have primitives	Theorem	Functions of a complex variable
Cardinality of a finite set	Concept	Mathematical logic and foundations
Mean value inequality	Theorem	Real functions
Sign of a permutation	Concept	Group theory and generalizations
Transposition	Definition	Group theory and generalizations
Open balls form a basis of the metric topology	Proposition	General topology
Rank of a product of matrices	Proposition	Linear and multilinear algebra; matrix theory
Transitive action	Concept	Group theory and generalizations
Existence of maximal ideals	Theorem	Commutative algebra
Nullcline	Concept	Ordinary differential equations
Isometries are injective	Proposition	General topology
Monotone sequence	Concept	Sequences, series, summability
Characteristic function of a sum of independent random variables	Proposition	Probability theory and stochastic processes
Power series of sine	Theorem	Special functions
Stationary distribution	Definition	Probability theory and stochastic processes
Fermat pseudoprime	Definition	Number theory