Nodes at W0, stub

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

Ideas 301–450 of 6044.

Name	Kind	Subject
Composition of continuous maps is continuous	Proposition	General topology
Mean squared error	Concept	Statistics
Derivative of arctangent	Proposition	Special functions
Matrix of a composition is the product of matrices	Theorem	Linear and multilinear algebra; matrix theory
Orthogonal family for a bilinear form	Definition	Linear and multilinear algebra; matrix theory
Additivity of the integral over intervals	Theorem	Real functions
Laplacian as a sum of second partial derivatives	Proposition	Partial differential equations
Number of edges of a complete graph	Proposition	Combinatorics
Harmonic numbers grow like log n	Theorem	Number theory
Left inverse	Concept	Mathematical logic and foundations
Negation of an existential statement	Theorem	Mathematical logic and foundations
Group of units of a ring	Definition	Associative rings and algebras
Equality of complex numbers	Proposition	Functions of a complex variable
Maximal ideals are prime	Corollary	Commutative algebra
Submodule	Concept	Associative rings and algebras
Jacobian of spherical coordinates	Proposition	Real functions
Number of derangements	Concept	Combinatorics
Subgroups of solvable groups are solvable	Proposition	Group theory and generalizations
Asymptotic stability	Definition	Ordinary differential equations
Composition of linear maps	Definition	Linear and multilinear algebra; matrix theory
Right coset	Definition	Group theory and generalizations
Trail	Definition	Combinatorics
Nilpotent endomorphism	Concept	Linear and multilinear algebra; matrix theory
Goldbach's conjecture	Conjecture	Number theory
Order of a zero	Definition	Functions of a complex variable
LaSalle's invariance principle	Theorem	Ordinary differential equations
Coprime ideals	Concept	Commutative algebra
Inclusion of a subspace is continuous	Proposition	General topology
Repeating decimals are rational	Theorem	Number theory
Arctangent	Definition	Special functions
Pole	Concept	Functions of a complex variable
Closed subsets of compact sets are compact	Proposition	General topology
The integers are countable	Proposition	Mathematical logic and foundations
Repeated roots and the derivative	Theorem	Commutative algebra
Tonelli's theorem	Theorem	Measure and integration
Existence of square roots of nonnegative reals	Theorem	Real functions
Closure in a metric space	Proposition	General topology
Diameter of a set	Definition	General topology
Uniqueness of splitting fields	Theorem	Field theory and polynomials
Partition of an interval	Definition	Real functions
Laplace expansion along a column	Theorem	Linear and multilinear algebra; matrix theory
Solution formula for linear first-order equations	Theorem	Ordinary differential equations
Strictly convex function	Definition	Real functions
Integral of the exponential function	Proposition	Real functions
Z[x] is not a principal ideal domain	Counterexample	Commutative algebra
Uniform metric on bounded functions	Example	Functional analysis
Linear map of a matrix	Concept	Linear and multilinear algebra; matrix theory
Dimension of a direct product	Proposition	Linear and multilinear algebra; matrix theory
Grassmann's formula	Theorem	Linear and multilinear algebra; matrix theory
Affine combination	Definition	Geometry
Multiplication of natural numbers	Concept	Mathematical logic and foundations
Real and imaginary parts	Concept	Functions of a complex variable
Regular curve	Definition	Differential geometry
Homogeneous system of linear equations	Definition	Linear and multilinear algebra; matrix theory
Convergence of a sequence in a metric space	Definition	General topology
Power series of the exponential function	Theorem	Special functions
The minimal polynomial divides every polynomial vanishing at the element	Proposition	Field theory and polynomials
Solution of a linear recurrence	Concept	Difference and functional equations
Every spanning set contains a basis	Theorem	Linear and multilinear algebra; matrix theory
Dimension of the annihilator	Proposition	Linear and multilinear algebra; matrix theory
cosh^2 - sinh^2 = 1	Proposition	Special functions
Units of the Gaussian integers	Proposition	Number theory
Number of invertible residues modulo n	Proposition	Number theory
Completion of a metric space	Concept	General topology
Continuous functions are Riemann integrable	Theorem	Real functions
Tangent function	Definition	Special functions
Sum of divisors	Concept	Number theory
Rayleigh quotient	Concept	Linear and multilinear algebra; matrix theory
Existence of Laurent expansions on an annulus	Theorem	Functions of a complex variable
Converse of Wilson's theorem	Proposition	Number theory
Geometric multiplicity	Definition	Linear and multilinear algebra; matrix theory
Continuous image of a closed interval is a closed interval	Corollary	Real functions
Geometric formula for the dot product	Proposition	Geometry
Linear isometry	Definition	Linear and multilinear algebra; matrix theory
Congruence is compatible with multiplication	Proposition	Number theory
Comparison of topologies	Concept	General topology
Limit of a product of sequences	Proposition	Sequences, series, summability
Cyclic groups of the same order are isomorphic	Theorem	Group theory and generalizations
Third isomorphism theorem for rings	Theorem	Associative rings and algebras
Associativity of matrix multiplication	Proposition	Linear and multilinear algebra; matrix theory
Tangent plane and normal vector of a surface	Concept	Differential geometry
Order of a pole	Concept	Functions of a complex variable
Kolmogorov's zero–one law	Theorem	Probability theory and stochastic processes
Correspondence between equivalence relations and partitions	Theorem	Mathematical logic and foundations
Separable equation	Concept	Ordinary differential equations
One-sided inverse of a square matrix is two-sided	Proposition	Linear and multilinear algebra; matrix theory
The reals have the cardinality of the continuum	Theorem	Mathematical logic and foundations
Uniqueness of the derivative	Proposition	Real functions
Even and odd permutations	Definition	Group theory and generalizations
Independent random variables are uncorrelated	Proposition	Probability theory and stochastic processes
Determinant of the inverse	Proposition	Linear and multilinear algebra; matrix theory
Continuity of the inverse of a strictly monotone continuous function	Theorem	Real functions
Group of units of a ring	Concept	Associative rings and algebras
Convolution of probability distributions	Definition	Probability theory and stochastic processes
Classification of finite abelian groups	Theorem	Group theory and generalizations
Lcm of coprime integers	Corollary	Number theory
Lipschitz maps are uniformly continuous	Proposition	Real functions
Incircle	Concept	Geometry
Disjoint cycles commute	Proposition	Group theory and generalizations
Composition of surjections is surjective	Proposition	Mathematical logic and foundations
Grönwall's inequality	Lemma	Real functions
Polynomials in several variables	Concept	Commutative algebra
Convex function on R^n	Concept	Real functions
A function with positive derivative is strictly increasing	Corollary	Real functions
Order on the integers	Concept	Order, lattices, ordered algebraic structures
Linear first-order equation	Concept	Ordinary differential equations
i squared is minus one	Proposition	Field theory and polynomials
If 2^p − 1 is prime then p is prime	Proposition	Number theory
Continuity at a point of a topological space	Definition	General topology
Fermat's Last Theorem for n = 3	Theorem	Number theory
Picard operator	Concept	Ordinary differential equations
Jordan block	Concept	Linear and multilinear algebra; matrix theory
Generalised eigenspace	Definition	Linear and multilinear algebra; matrix theory
Subfield	Definition	Field theory and polynomials
Third isomorphism theorem for vector spaces	Theorem	Linear and multilinear algebra; matrix theory
Uniform continuity on a set	Concept	Real functions
Divisibility in a commutative ring	Concept	Commutative algebra
Equation of a plane	Concept	Geometry
Linear isometry	Concept	Linear and multilinear algebra; matrix theory
Derivatives of the hyperbolic functions	Proposition	Special functions
Distance from a point to a set	Definition	General topology
Trajectory	Concept	Dynamical systems and ergodic theory
Solution of an ordinary differential equation	Concept	Ordinary differential equations
Derivative of the logarithm	Theorem	Special functions
Algebra of limits	Concept	Sequences, series, summability
Image of a set	Concept	Mathematical logic and foundations
Differentiable functions are continuous	Proposition	Real functions
Anticommutativity of the cross product	Proposition	Linear and multilinear algebra; matrix theory
Every integer is a square times a square-free integer	Proposition	Number theory
Linearity of the integral	Theorem	Real functions
Phase line	Concept	Ordinary differential equations
Finite p-groups are nilpotent	Theorem	Group theory and generalizations
Directrix	Definition	Geometry
Holomorphic functions are analytic	Theorem	Functions of a complex variable
Absolutely convergent series in a Banach space converge	Theorem	Sequences, series, summability
Successor function	Definition	Mathematical logic and foundations
Number of prime factors counted with multiplicity	Definition	Number theory
Higher derivative	Definition	Real functions
P-adic valuation of a product	Proposition	Number theory
Walk	Concept	Combinatorics
Group isomorphism	Definition	Group theory and generalizations
Mean of the Poisson distribution	Proposition	Probability theory and stochastic processes
Chevalley–Warning theorem	Theorem	Number theory
Spanning set	Concept	Linear and multilinear algebra; matrix theory
Cyclic subgroup generated by an element	Concept	Group theory and generalizations
Divergence part of the ratio test	Proposition	Sequences, series, summability
Class equation	Theorem	Group theory and generalizations
Product of primitive polynomials is primitive	Theorem	Commutative algebra
Existence of an eigenvalue over an algebraically closed field	Theorem	Linear and multilinear algebra; matrix theory
Equinumerous sets	Definition	Mathematical logic and foundations