Every idea

Ideas 1501–1650 of 7806.

Name	Kind	Subject
A finite integral domain is a field	Theorem	Commutative algebra
The multiplicative group of a finite field is cyclic	Corollary	Field theory and polynomials
Exact equation	Definition	Ordinary differential equations
Empty set	Object	Mathematical logic and foundations
Interval of convergence	Concept	Functions of a complex variable
Counterexample	Concept	General and overarching topics
Existence of the infimum	Theorem	Real functions
Hamiltonian system	Concept	Dynamical systems and ergodic theory
Neyman–Pearson lemma	Lemma	Statistics
Rule of sum	Theorem	Combinatorics
Continuity at a point	Definition	Real functions
Refinement of a partition	Definition	Real functions
Limit cycle	Definition	Ordinary differential equations
Concave function	Definition	Real functions
Convergence in probability	Definition	Probability theory and stochastic processes
Proof by infinite descent	Concept	Number theory
Primality test	Concept	Number theory
Formal derivative	Concept	Commutative algebra
Boole's inequality	Theorem	Probability theory and stochastic processes
Prime number theorem	Theorem	Number theory
Liouville's theorem	Theorem	Functions of a complex variable
Primitive root of unity	Concept	Number theory
Binomial theorem	Theorem	Combinatorics
P-value	Definition	Statistics
Universal property of the abelianisation	Theorem	Group theory and generalizations
Normal convergence	Concept	Sequences, series, summability
Epsilon-delta continuity in metric spaces	Proposition	General topology
Hermitian matrix	Definition	Linear and multilinear algebra; matrix theory
Orientable surface	Definition	Differential geometry
Existence of nontrivial solutions of Pell's equation	Theorem	Number theory
Chi-squared test	Concept	Statistics
Inverse in terms of the adjugate	Corollary	Linear and multilinear algebra; matrix theory
Normal operator	Definition	Operator theory
Invariant subspace	Definition	Linear and multilinear algebra; matrix theory
Row space	Definition	Linear and multilinear algebra; matrix theory
Function	Concept	Mathematical logic and foundations
Continuous image of a connected set is connected	Proposition	General topology
Convergence in probability implies convergence in distribution	Theorem	Probability theory and stochastic processes
Linear subspace	Definition	Linear and multilinear algebra; matrix theory
Constrained optimisation	Concept	Operations research, mathematical programming
Central limit theorem	Theorem	Probability theory and stochastic processes
Hyperbolic cosine	Definition	Special functions
Locally compact space	Definition	General topology
Field extension	Concept	Field theory and polynomials
Homogeneous linear equation	Definition	Ordinary differential equations
Induced subgraph	Concept	Combinatorics
QR decomposition	Theorem	Linear and multilinear algebra; matrix theory
Imaginary unit	Object	Field theory and polynomials
Divisibility by 9	Proposition	Number theory
Collinear points	Definition	Geometry
Existence of an algebraic closure	Theorem	Field theory and polynomials
Gershgorin circle theorem	Theorem	Linear and multilinear algebra; matrix theory
Linear independence	Definition	Linear and multilinear algebra; matrix theory
Poincaré–Bendixson theorem	Theorem	Ordinary differential equations
Beta distribution	Concept	Probability theory and stochastic processes
Domain in the complex plane	Concept	Functions of a complex variable
Rank of a matrix	Definition	Linear and multilinear algebra; matrix theory
Impossibility of trisecting the angle	Theorem	Field theory and polynomials
Conjugate transpose	Definition	Linear and multilinear algebra; matrix theory
Product of vector spaces	Concept	Linear and multilinear algebra; matrix theory
The exponential function is its own derivative	Theorem	Special functions
Iterated derivative	Definition	Real functions
68–95–99.7 rule	Example	Probability theory and stochastic processes
Element	Definition	Mathematical logic and foundations
Cantor's intersection theorem	Theorem	General topology
x sin(1/x) is continuous at 0	Example	Real functions
Lower triangular matrix	Definition	Linear and multilinear algebra; matrix theory
Cauchy's integral formula for derivatives	Theorem	Functions of a complex variable
Set bounded above	Concept	Order, lattices, ordered algebraic structures
Prime elements are irreducible in an integral domain	Proposition	Commutative algebra
Column space	Definition	Linear and multilinear algebra; matrix theory
Closed and exact forms	Definition	Global analysis, analysis on manifolds
Well-order	Definition	Order, lattices, ordered algebraic structures
Transition matrix	Definition	Probability theory and stochastic processes
Subsequence	Concept	Sequences, series, summability
Conditional variance	Definition	Probability theory and stochastic processes
Derivative	Definition	Real functions
Row echelon form	Definition	Linear and multilinear algebra; matrix theory
Field of fractions	Concept	Commutative algebra
Riemann integrable function	Concept	Real functions
Lyapunov stability	Concept	Ordinary differential equations
Superposition principle	Proposition	Ordinary differential equations
Iterated derivative	Concept	Real functions
Primitive root modulo n	Concept	Number theory
Bounded linear maps are continuous	Theorem	Operator theory
Mersenne prime	Concept	Number theory
Derivative vanishes at a local extremum	Theorem	Real functions
Transition matrix	Concept	Probability theory and stochastic processes
Divisors of a natural number	Concept	Number theory
Quadratic integer	Concept	Number theory
Outcome	Concept	Probability theory and stochastic processes
Divergence of a curl is zero	Proposition	Real functions
g to the n equals 1 iff the order divides n	Proposition	Group theory and generalizations
Characteristic of a ring	Concept	Commutative algebra
Order on the integers	Definition	Order, lattices, ordered algebraic structures
Disjunction	Concept	Mathematical logic and foundations
Cayley–Hamilton theorem	Theorem	Linear and multilinear algebra; matrix theory
Square root	Concept	Real functions
Greatest common divisor in an integral domain	Definition	Commutative algebra
Graph isomorphism	Concept	Combinatorics
Convolution of probability distributions	Concept	Probability theory and stochastic processes
Group of units of Z/nZ	Object	Number theory
Double counting	Concept	Combinatorics
Circumcentre	Concept	Geometry
Codomain	Definition	Mathematical logic and foundations
Absolutely convergent improper integral	Concept	Sequences, series, summability
Möbius function	Concept	Number theory
Local maximum	Concept	Real functions
Affine subspace	Definition	Geometry
Closed subsets of complete spaces are complete	Proposition	General topology
Evaluation homomorphism	Concept	Commutative algebra
Exponent of a group	Definition	Group theory and generalizations
General linear group	Object	Group theory and generalizations
Divisors of a natural number	Definition	Number theory
The gamma function extends the factorial	Theorem	Special functions
Reachability	Concept	Combinatorics
Locally compact space	Concept	General topology
Subset	Definition	Mathematical logic and foundations
A subgroup whose index is the smallest prime divisor of the order is normal	Theorem	Group theory and generalizations
e as the limit of (1 + 1/n)^n	Proposition	Real functions
Twin prime conjecture	Conjecture	Number theory
Universal property of the quotient topology	Theorem	General topology
Ellipse	Definition	Geometry
Inclusion–exclusion principle	Theorem	Combinatorics
Affine span	Definition	Geometry
Connected graph	Definition	Combinatorics
Construction of the rationals as fractions	Concept	Commutative algebra
Absolute value	Concept	Real functions
Kurtosis	Concept	Statistics
Preimage of a set	Definition	Mathematical logic and foundations
The reals form a field	Theorem	Field theory and polynomials
Characterization of bridges	Theorem	Combinatorics
Epsilon-delta uniform continuity	Proposition	General topology
Matrix ring	Object	Linear and multilinear algebra; matrix theory
Group of units of a monoid	Concept	Group theory and generalizations
Conditional probability	Definition	Probability theory and stochastic processes
Chromatic number of a complete bipartite graph	Proposition	Combinatorics
Bertrand's postulate	Theorem	Number theory
Maximum degree	Concept	Combinatorics
Triangle inequality for norms	Proposition	Functional analysis
Simultaneous diagonalisation	Theorem	Linear and multilinear algebra; matrix theory
Monotone convergence theorem for sequences	Theorem	Sequences, series, summability
Burnside's p^a q^b theorem	Theorem	Group theory and generalizations
Constructible number	Definition	Field theory and polynomials
Total derivative	Concept	Real functions
Chinese remainder theorem	Theorem	Number theory
Even and odd functions	Concept	Real functions
Scalar potential	Definition	Real functions
Lévy's continuity theorem	Theorem	Probability theory and stochastic processes
Reduced word	Definition	Group theory and generalizations