Nodes at W0, stub

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

Ideas 1501–1650 of 6044.

Name	Kind	Subject
Norm on the Gaussian integers	Concept	Number theory
Integration by partial fractions	Concept	Real functions
Proof by cases	Concept	General and overarching topics
Trace of a linear map is the trace of its matrix	Proposition	Linear and multilinear algebra; matrix theory
R/M is a field iff M is maximal	Theorem	Commutative algebra
x^2 sin(1/x) is differentiable with discontinuous derivative	Counterexample	Real functions
Probability mass function	Definition	Probability theory and stochastic processes
Reduced row echelon form	Concept	Linear and multilinear algebra; matrix theory
Local maximum and minimum	Concept	Real functions
Two-element Boolean algebra	Example	Order, lattices, ordered algebraic structures
A subspace of full dimension is the whole space	Proposition	Linear and multilinear algebra; matrix theory
Circle as a quotient of the real line	Example	General topology
There is a natural number n with 1/n below any positive epsilon	Corollary	Real functions
Invariant factors and elementary divisors	Concept	Group theory and generalizations
Taylor's theorem with the integral remainder	Theorem	Approximations and expansions
Product of exponentials	Theorem	Special functions
Volume of a ball in R^3	Proposition	Real functions
A prime is a Gaussian prime if and only if it is 3 modulo 4	Theorem	Number theory
Hoeffding's inequality	Theorem	Probability theory and stochastic processes
Pole	Definition	Functions of a complex variable
Distance from a point to a set	Concept	General topology
Moment-generating function of a sum of independent random variables	Proposition	Probability theory and stochastic processes
Image of a linear map	Concept	Linear and multilinear algebra; matrix theory
Nullcline	Definition	Ordinary differential equations
Right inverse	Concept	Mathematical logic and foundations
Group of nth roots of unity	Object	Group theory and generalizations
Gram–Schmidt vectors are orthogonal	Proposition	Linear and multilinear algebra; matrix theory
A monotone function has countably many discontinuities	Theorem	Real functions
Determinant of a linear map	Concept	Linear and multilinear algebra; matrix theory
Number of injections	Theorem	Combinatorics
Complex logarithm	Definition	Special functions
Hall's theorem for bipartite graphs	Theorem	Combinatorics
Discrete random variable	Concept	Probability theory and stochastic processes
Countable intersection of dense open sets is dense	Proposition	General topology
The exterior derivative squares to zero	Theorem	Global analysis, analysis on manifolds
Path component	Concept	General topology
Congruent triangles	Definition	Geometry
Idempotent element	Definition	Associative rings and algebras
Forced oscillation and resonance	Example	Mechanics of particles and systems
Consistent and inconsistent systems	Concept	Linear and multilinear algebra; matrix theory
Impossibility of squaring the circle	Theorem	Field theory and polynomials
Continuity of probability measures	Proposition	Probability theory and stochastic processes
Space of linear maps	Concept	Linear and multilinear algebra; matrix theory
Handshaking lemma	Theorem	Combinatorics
Number of elements of each order in a cyclic group	Theorem	Group theory and generalizations
Monotonicity of the cumulative distribution function	Proposition	Probability theory and stochastic processes
Even and odd functions	Definition	Real functions
Euler's partition theorem	Theorem	Combinatorics
Archimedean ordered field	Concept	Field theory and polynomials
K-colourable graph	Concept	Combinatorics
Consistent estimator	Definition	Statistics
Order of a differential equation	Concept	Ordinary differential equations
Decomposition of a permutation into transpositions	Theorem	Group theory and generalizations
Length of a vector	Concept	Geometry
Periodic continued fraction	Definition	Number theory
Coordinate space	Object	Linear and multilinear algebra; matrix theory
Cofactor	Concept	Linear and multilinear algebra; matrix theory
Greatest element	Concept	Order, lattices, ordered algebraic structures
Method of undetermined coefficients	Concept	Ordinary differential equations
Eisenstein's lemma	Lemma	Number theory
Cluster point of a sequence	Concept	Sequences, series, summability
The principal logarithm is holomorphic off the branch cut	Proposition	Special functions
Upper central series	Concept	Group theory and generalizations
A root of an integer is an integer or irrational	Theorem	Number theory
De Morgan's laws in a Boolean algebra	Proposition	Order, lattices, ordered algebraic structures
Direct sum of subspaces	Concept	Linear and multilinear algebra; matrix theory
Absolutely convergent series converge	Theorem	Sequences, series, summability
Limit at infinity	Definition	Real functions
Catalan recurrence	Theorem	Combinatorics
Orthogonal vectors	Concept	Linear and multilinear algebra; matrix theory
Gauss–Wantzel theorem	Theorem	Field theory and polynomials
Series of functions	Concept	Sequences, series, summability
The order modulo p divides p − 1	Corollary	Number theory
Trace of a product is symmetric	Proposition	Linear and multilinear algebra; matrix theory
Level set	Definition	Real functions
Tail sum formula for expectation	Proposition	Probability theory and stochastic processes
Order isomorphism	Definition	Order, lattices, ordered algebraic structures
K-colourable graph	Definition	Combinatorics
Existence of an orthonormal basis	Theorem	Linear and multilinear algebra; matrix theory
Sequence of functions	Concept	Sequences, series, summability
Distinct eigenvalues imply diagonalisable	Corollary	Linear and multilinear algebra; matrix theory
Binary trees are counted by Catalan numbers	Theorem	Combinatorics
Second derivative	Definition	Real functions
Order on the natural numbers	Definition	Mathematical logic and foundations
Characteristic polynomial of a linear recurrence	Concept	Difference and functional equations
Primitive element of a finite field	Definition	Field theory and polynomials
Absorbing Markov chain	Definition	Probability theory and stochastic processes
Comparability of cardinals	Theorem	Mathematical logic and foundations
Groups of order pq	Example	Group theory and generalizations
Term-by-term integration	Theorem	Sequences, series, summability
Matrix exponential as the solution of a linear system	Theorem	Ordinary differential equations
Open map	Concept	General topology
Universal property of the tensor product	Theorem	Linear and multilinear algebra; matrix theory
Combinations with repetition	Definition	Combinatorics
Similar triangles	Concept	Geometry
Continuity via open sets	Theorem	General topology
Normaliser	Concept	Group theory and generalizations
Sum of independent Poisson random variables	Proposition	Probability theory and stochastic processes
Irrationality of the square root of a prime	Theorem	Number theory
Integers modulo n as a quotient group	Example	Group theory and generalizations
Order of a pole	Definition	Functions of a complex variable
Existence of nth roots of complex numbers	Theorem	Field theory and polynomials
Power series are holomorphic in the disc of convergence	Theorem	Functions of a complex variable
Flux through a surface	Definition	Real functions
Fundamental theorem of contour integration	Theorem	Functions of a complex variable
Orbit	Concept	Group theory and generalizations
Matrix of a linear map	Concept	Linear and multilinear algebra; matrix theory
Closed balls are closed	Proposition	General topology
x^n converges pointwise but not uniformly on [0, 1]	Counterexample	Sequences, series, summability
Cyclic subgroup generated by an element	Definition	Group theory and generalizations
Dyck word	Concept	Computer science
Conditional probability distribution	Definition	Probability theory and stochastic processes
Metric topology	Concept	General topology
Homotopy invariance of line integrals of closed forms	Theorem	Real functions
Number of distinct prime factors	Definition	Number theory
Decomposition of a permutation into disjoint cycles	Theorem	Group theory and generalizations
Tangent plane to a graph	Definition	Real functions
Quadratic reciprocity for the Jacobi symbol	Theorem	Number theory
Matrix of a linear map	Definition	Linear and multilinear algebra; matrix theory
Determinant as a group homomorphism	Example	Linear and multilinear algebra; matrix theory
Power series of complex cosine	Proposition	Special functions
Diagonalisation of a quadratic form	Theorem	Number theory
Decomposition into generalised eigenspaces	Theorem	Linear and multilinear algebra; matrix theory
Linear first-order equation	Definition	Ordinary differential equations
Intermediate field	Concept	Field theory and polynomials
A function with nonnegative second derivative is convex	Corollary	Real functions
Determinant of the identity matrix	Proposition	Linear and multilinear algebra; matrix theory
Proper metric space	Definition	General topology
Interval of convergence	Definition	Functions of a complex variable
Greatest element	Definition	Order, lattices, ordered algebraic structures
Computing the inverse by row reduction	Concept	Linear and multilinear algebra; matrix theory
The complex conjugate is not holomorphic	Counterexample	Functions of a complex variable
Local homeomorphism from the inverse function theorem	Corollary	Real functions
Countable union of countable sets is countable	Theorem	Mathematical logic and foundations
Probability-generating function	Definition	Probability theory and stochastic processes
Constant multiple rule	Corollary	Real functions
Dimension of the space of linear maps	Proposition	Linear and multilinear algebra; matrix theory
Cauchy criterion for sequences	Theorem	Sequences, series, summability
Greatest common divisor in an integral domain	Concept	Commutative algebra
Memorylessness	Concept	Probability theory and stochastic processes
Pairwise independence	Concept	Probability theory and stochastic processes
A complex number times its conjugate	Proposition	Functions of a complex variable
Gradient points in the direction of steepest ascent	Proposition	Real functions
Orbits partition the set	Proposition	Group theory and generalizations
Jacobian determinant	Concept	Real functions
Neighbourhood	Concept	Combinatorics
Tangent vector of a curve	Concept	Differential geometry
Angle at a point	Definition	Geometry
Angle between two vectors	Concept	Geometry
g to the order of the group is the identity	Corollary	Group theory and generalizations