Every idea

Ideas 151–300 of 7806.

Name	Kind	Subject
Well-order	Concept	Order, lattices, ordered algebraic structures
The complex numbers cannot be ordered	Theorem	Field theory and polynomials
Characteristic subgroup	Definition	Group theory and generalizations
Totally disconnected space	Definition	General topology
Periodic orbit	Definition	Ordinary differential equations
Ramsey number	Definition	Combinatorics
Normality via left and right cosets	Proposition	Group theory and generalizations
Public-key cryptography	Concept	Information and communication theory, circuits
Inner product space	Definition	Linear and multilinear algebra; matrix theory
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
Urysohn's lemma	Lemma	General topology
Composition of injections is injective	Proposition	Mathematical logic and foundations
Pythagorean triple	Definition	Number theory
Periodic continued fraction	Concept	Number theory
Order of cardinals	Definition	Mathematical logic and foundations
Generalised eigenvector	Concept	Linear and multilinear algebra; matrix theory
Divergent sequence	Definition	Sequences, series, summability
Equivalence classes form a partition	Theorem	Mathematical logic and foundations
Maximal solution	Concept	Ordinary differential equations
Legendre symbol	Definition	Number theory
Vandermonde's identity	Theorem	Combinatorics
Regular polygon	Concept	Geometry
Multigraph	Definition	Combinatorics
Triangle inequality for a metric	Axiom	General topology
Antisymmetric relation	Definition	Mathematical logic and foundations
Infinite set	Definition	Mathematical logic and foundations
Positive semidefinite matrix	Concept	Linear and multilinear algebra; matrix theory
Cauchy's integral theorem	Theorem	Functions of a complex variable
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
Isolated point	Definition	General topology
Similar triangles	Definition	Geometry
Hyperbolic functions	Concept	Special functions
Spherical coordinates	Concept	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
Tangent line	Concept	Real functions
Definite and indefinite quadratic forms	Concept	Linear and multilinear algebra; matrix theory
Elementary matrix	Concept	Linear and multilinear algebra; matrix theory
Lyapunov function	Concept	Ordinary differential equations
Residue class	Concept	Number theory
Surjective function	Concept	Mathematical logic and foundations
Composition of relations	Definition	Mathematical logic and foundations
Neighbourhood	Definition	Combinatorics
Integrating factor	Definition	Ordinary differential equations
Diffie–Hellman key exchange	Example	Information and communication theory, circuits
Hyperbolic equilibrium point	Concept	Dynamical systems and ergodic theory
Countable set	Concept	Mathematical logic and foundations
Orthogonal family for a bilinear form	Concept	Linear and multilinear algebra; matrix theory
Symmetry of second derivatives	Theorem	Real functions
Bijective iff it has a two-sided inverse	Proposition	Mathematical logic and foundations
Prime element	Concept	Commutative algebra
Quadratic integer	Definition	Number theory
Uniqueness of the algebraic closure	Theorem	Field theory and polynomials
Cantor set is closed	Proposition	General topology
Connected component	Definition	Combinatorics
Arguments add under multiplication	Theorem	Functions of a complex variable
Central binomial coefficient	Definition	Combinatorics
Legendre's formula	Theorem	Number theory
Cassini's identity	Theorem	Number theory
Geometric series	Example	Sequences, series, summability
Identically distributed random variables	Definition	Probability theory and stochastic processes
Moment	Concept	Probability theory and stochastic processes
Uniformly Cauchy sequence of functions	Definition	Sequences, series, summability
Constructive proof	Concept	Mathematical logic and foundations
Limit at infinity	Concept	Real functions
Open set	Definition	General topology
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
Carathéodory's theorem	Theorem	Convex and discrete geometry
Euler's theorem on Eulerian circuits	Theorem	Combinatorics
Existence of prime factorization	Theorem	Number theory
Matrix exponential	Concept	Linear and multilinear algebra; matrix theory
Totally bounded set	Concept	General topology
Free group	Definition	Group theory and generalizations
Definite integral	Definition	Real functions
Darboux and Riemann integrals agree	Theorem	Real functions
Taylor series	Definition	Approximations and expansions
Order of cardinals	Concept	Mathematical logic and foundations
Well-founded relation	Definition	Mathematical logic and foundations
Euclidean algorithm in a Euclidean domain	Concept	Commutative algebra
Left inverse	Definition	Mathematical logic and foundations
Reflection	Definition	Linear and multilinear algebra; matrix theory
Uniqueness of solutions for Lipschitz vector fields	Theorem	Ordinary differential equations
Conjunction	Concept	Mathematical logic and foundations
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
Parallelogram law	Proposition	Functional analysis
Flux through a surface	Concept	Real functions
Density of the normal distribution	Definition	Probability theory and stochastic processes
Derivative function	Definition	Real functions
Similar matrices	Definition	Linear and multilinear algebra; matrix theory
Reflection in a line or plane	Definition	Geometry
Quotients of solvable groups are solvable	Proposition	Group theory and generalizations
Associate elements	Concept	Commutative algebra
Angle addition formulas	Theorem	Special functions
Exponential distribution	Definition	Probability theory and stochastic processes
Flow of a vector field	Definition	Dynamical systems and ergodic theory
Euclid's theorem	Theorem	Number theory
Vector field	Concept	Real functions
Negation	Concept	Mathematical logic and foundations
Planar graph	Definition	Combinatorics
Binary tree	Definition	Combinatorics
Holomorphic functions on a disc have primitives	Theorem	Functions of a complex variable
Convex set	Concept	Convex and discrete geometry
Infinite cyclic group	Example	Group theory and generalizations
Open set	Concept	General topology
Eisenstein's criterion	Theorem	Field theory and polynomials
Covariance matrix	Definition	Statistics
Edge colouring	Definition	Combinatorics
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
Free module	Definition	Associative rings and algebras
Power of a point	Concept	Geometry
Open balls form a basis of the metric topology	Proposition	General topology
Prime factorization	Concept	Number theory
Rank of a product of matrices	Proposition	Linear and multilinear algebra; matrix theory
Transitive action	Concept	Group theory and generalizations
Newton's law of cooling	Example	Classical thermodynamics, heat transfer
Casorati–Weierstrass theorem	Theorem	Functions of a complex variable
Existence of maximal ideals	Theorem	Commutative algebra
Isometry	Concept	General topology
Nullcline	Concept	Ordinary differential equations
Inverse trigonometric functions	Definition	Special functions
Chebyshev's inequality	Theorem	Probability theory and stochastic processes
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
Polynomial evaluation	Concept	Commutative algebra
Discrete uniform distribution	Concept	Probability theory and stochastic processes
Intermediate field	Definition	Field theory and polynomials
Divergence	Definition	Real functions
Splitting field	Definition	Field theory and polynomials
The complex exponential is 2πi-periodic	Proposition	Special functions
Sum of the roots of unity	Proposition	Number theory
Complex logarithm	Concept	Special functions
Line integral of a scalar field	Concept	Real functions
Multiplicative order	Concept	Number theory
Higher partial derivatives	Definition	Real functions
Algebraically closed field	Definition	Field theory and polynomials