Every idea

Ideas 3001–3150 of 7806.

Name	Kind	Subject
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
Coprime integers	Concept	Number theory
Compact closed unit ball implies finite dimension	Theorem	Functional analysis
Orthogonal matrix	Concept	Linear and multilinear algebra; matrix theory
Cyclotomic polynomial	Definition	Number theory
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
Riemann integral	Concept	Real functions
Cofactor	Definition	Linear and multilinear algebra; matrix theory
Absolute convergence	Definition	Sequences, series, summability
Line integral as an integral over the parameter interval	Theorem	Real functions
Complete subspaces are closed	Proposition	General topology
Sesquilinear form	Definition	Linear and multilinear algebra; matrix theory
Convergent sequence	Concept	Sequences, series, summability
Rank–nullity theorem	Theorem	Linear and multilinear algebra; matrix theory
Irrationality of e	Theorem	Number theory
Disjoint sets	Definition	Mathematical logic and foundations
Unique factorisation domain	Concept	Commutative algebra
Trail	Concept	Combinatorics
Addition of natural numbers	Definition	Mathematical logic and foundations
Harmonic function	Definition	Potential theory
Law of total probability for an event and its complement	Corollary	Probability theory and stochastic processes
Dual basis	Definition	Linear and multilinear algebra; matrix theory
Inverse function	Definition	Mathematical logic and foundations
Normal subgroup	Definition	Group theory and generalizations
Uncountable set	Concept	Mathematical logic and foundations
Sample space	Definition	Probability theory and stochastic processes
Transpose	Definition	Linear and multilinear algebra; matrix theory
Kernel of a homomorphism	Concept	Group theory and generalizations
Tangent half-angle substitution	Concept	Real functions
Branch cut	Concept	Functions of a complex variable
Epsilon-delta definition of continuity	Proposition	Real functions
Fermat pseudoprime	Concept	Number theory
Equivalence class	Concept	Mathematical logic and foundations
Chinese remainder theorem for rings	Theorem	Commutative algebra
Time translation of solutions of an autonomous system	Proposition	Ordinary differential equations
Double integral	Concept	Real functions
Congruence modulo n	Concept	Number theory
Sine and cosine	Definition	Special functions
Orthocentre	Concept	Geometry
Path-connected space	Concept	General topology
Subgraph	Concept	Combinatorics
Norm on the Gaussian integers	Concept	Number theory
Integration by partial fractions	Concept	Real functions
Cardinality of the continuum	Object	Mathematical logic and foundations
Clique number	Definition	Combinatorics
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
Binomial distribution	Concept	Probability theory and stochastic processes
Separable extension	Concept	Field theory and polynomials
Group action	Concept	Group theory and generalizations
Rational function	Definition	Real functions
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
Cauchy–Euler equation	Definition	Ordinary differential equations
Order of an element	Concept	Group theory and generalizations
Totally bounded set	Definition	General topology
Euclid–Euler theorem	Theorem	Number theory
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
Factorial	Definition	Combinatorics
Ordered pair	Concept	Mathematical logic and foundations
Sylvester's law of inertia	Theorem	Linear and multilinear algebra; matrix theory
Monotone function	Definition	Order, lattices, ordered algebraic structures
Gambler's ruin	Problem	Probability theory and stochastic processes
Inverse hyperbolic functions	Concept	Special functions
Newton's identities	Theorem	Combinatorics
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
Continuous uniform distribution	Definition	Probability theory and stochastic processes
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
Free abelian group	Concept	Group theory and generalizations
Dimension theorem for vector spaces	Theorem	Linear and multilinear algebra; matrix theory
Sylvester's criterion	Theorem	Linear and multilinear algebra; matrix theory
Fermat number	Concept	Number theory
Cholesky decomposition	Theorem	Linear and multilinear algebra; matrix theory
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
Indefinite integral	Concept	Real functions
Hyperbola	Concept	Geometry
Edge set	Definition	Combinatorics
Hoeffding's inequality	Theorem	Probability theory and stochastic processes
Pole	Definition	Functions of a complex variable
Distance in a graph	Definition	Combinatorics
Distance from a point to a set	Concept	General topology
Field extension	Definition	Field theory and polynomials
Surface area	Definition	Measure and integration
Normal vector	Concept	Geometry
Expected value	Concept	Probability theory and stochastic processes
Moment-generating function	Concept	Probability theory and stochastic processes
Borel sigma-algebra	Concept	Measure and integration
Moment-generating function of a sum of independent random variables	Proposition	Probability theory and stochastic processes
Extreme value theorem	Theorem	Real functions
Subspace topology	Concept	General topology
Image of a linear map	Concept	Linear and multilinear algebra; matrix theory
Cantor's theorem	Theorem	Mathematical logic and foundations
Nullcline	Definition	Ordinary differential equations
Bell numbers	Definition	Number theory
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
Iterated integral	Concept	Real functions
Hölder continuity	Definition	Real functions
Division ring	Definition	Field theory and polynomials
Boolean function	Concept	Order, lattices, ordered algebraic structures
Determinant of a linear map	Concept	Linear and multilinear algebra; matrix theory
Number of injections	Theorem	Combinatorics
Union	Concept	Mathematical logic and foundations
Subgroup	Concept	Group theory and generalizations
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
Continuous function	Concept	Real functions
Laurent series	Definition	Functions of a complex variable
Hypergeometric distribution	Concept	Probability theory and stochastic processes
Cayley transform	Example	Functions of a complex variable
Idempotent element	Definition	Associative rings and algebras
Forced oscillation and resonance	Example	Mechanics of particles and systems
Tietze extension theorem	Theorem	General topology
Uncountable set	Definition	Mathematical logic and foundations
Elementary symmetric polynomial	Concept	Combinatorics
Quantile function	Concept	Probability theory and stochastic processes
Algebraic closure	Concept	Field theory and polynomials
Hyperbolic tangent	Concept	Special functions
Consistent and inconsistent systems	Concept	Linear and multilinear algebra; matrix theory
Impossibility of squaring the circle	Theorem	Field theory and polynomials
Centroid	Concept	Geometry
Arc length	Definition	Real functions
Winding number	Definition	Algebraic topology
Altitude of a triangle	Definition	Geometry
Continuity of probability measures	Proposition	Probability theory and stochastic processes
Reflexive relation	Concept	Mathematical logic and foundations
Space of linear maps	Concept	Linear and multilinear algebra; matrix theory
Uniform limit theorem	Theorem	Sequences, series, summability
Boolean algebra	Concept	Order, lattices, ordered algebraic structures