Examples

An instance of a concept.

Ideas 1–150 of 431.

Name	Kind	Subject
Power set Boolean algebra	Example	Order, lattices, ordered algebraic structures
Zero ring	Example	Associative rings and algebras
Exponential growth and decay	Example	Ordinary differential equations
Lotka–Volterra equations	Example	Biology and other natural sciences
Diffie–Hellman key exchange	Example	Information and communication theory, circuits
Geometric series	Example	Sequences, series, summability
Infinite cyclic group	Example	Group theory and generalizations
Newton's law of cooling	Example	Classical thermodynamics, heat transfer
Integral of exp(-x) over the half line	Example	Sequences, series, summability
Torus	Example	Manifolds and cell complexes
Complete graph	Example	Combinatorics
Möbius strip	Example	Manifolds and cell complexes
The dihedral group of order 8	Example	Group theory and generalizations
The rationals as the field of fractions of the integers	Example	Commutative algebra
Uniform metric on bounded functions	Example	Functional analysis
Path graph	Example	Combinatorics
Taxicab metric	Example	Geometry
Circulant matrix	Example	Linear and multilinear algebra; matrix theory
Sequence spaces lp	Example	Functional analysis
The sequence 1/n tends to zero	Example	Sequences, series, summability
Tower of Hanoi	Example	General and overarching topics
The symmetric group S3	Example	Group theory and generalizations
The nth root of n tends to 1	Example	Sequences, series, summability
Action on left cosets	Example	Group theory and generalizations
Cofinite topology	Example	General topology
Rotation matrix	Example	Linear and multilinear algebra; matrix theory
Trivial group	Example	Group theory and generalizations
Additive group of integers	Example	Group theory and generalizations
Cantor set	Example	General topology
Logistic equation	Example	Biology and other natural sciences
Harmonic series	Example	Sequences, series, summability
Gaussian integral	Example	Real functions
Euclidean metric	Example	Geometry
Base rate fallacy	Example	Statistics
Blow-up in finite time	Example	Ordinary differential equations
68–95–99.7 rule	Example	Probability theory and stochastic processes
x sin(1/x) is continuous at 0	Example	Real functions
Cyclic group of order n	Example	Group theory and generalizations
Sum of the reciprocals of the factorials	Example	Sequences, series, summability
Fibonacci sequence	Example	Number theory
The quaternions	Example	Associative rings and algebras
The alternating group A5 is simple	Example	Group theory and generalizations
Decimal expansion as a series	Example	Sequences, series, summability
Function space	Example	Linear and multilinear algebra; matrix theory
Dirichlet integral	Example	Real functions
Binomial series	Example	Functions of a complex variable
Thomae's function	Example	Real functions
RSA cryptosystem	Example	Information and communication theory, circuits
Existence of nth roots by the intermediate value theorem	Example	Real functions
Space of polynomials of bounded degree	Example	Linear and multilinear algebra; matrix theory
The ring of integers	Example	Commutative algebra
Alternating harmonic series	Example	Sequences, series, summability
Action by left multiplication	Example	Group theory and generalizations
p-norm on R^n	Example	Functional analysis
Usual metric on the real line	Example	General topology
Hilbert's hotel	Example	Mathematical logic and foundations
Discrete metric	Example	General topology
exp(1/z) has an essential singularity at 0	Example	Functions of a complex variable
Birthday problem	Example	Probability theory and stochastic processes
0.999... equals 1	Example	Number theory
Cantor pairing function	Example	Mathematical logic and foundations
Petersen graph	Example	Combinatorics
Action by conjugation	Example	Group theory and generalizations
Sup norm on bounded continuous functions	Example	Functional analysis
The sequence r^n tends to zero for \|r\| < 1	Example	Sequences, series, summability
Cycle graph	Example	Combinatorics
Geometric series as a power series	Example	Commutative algebra
Space of matrices	Example	Linear and multilinear algebra; matrix theory
Damped harmonic oscillator	Example	Mechanics of particles and systems
Discrete topology	Example	General topology
Pendulum equation	Example	Mechanics of particles and systems
Differentiation as a linear map	Example	Linear and multilinear algebra; matrix theory
Integral of 1/z around the unit circle	Example	Functions of a complex variable
Bertrand paradox	Example	Probability theory and stochastic processes
Clairaut's equation	Example	Ordinary differential equations
p-metric on R^n	Example	Functional analysis
The sequence r^n tends to infinity for r > 1	Example	Sequences, series, summability
Complete bipartite graph	Example	Combinatorics
Improper integral of x^p on an unbounded interval	Example	Sequences, series, summability
Sup metric on R^n	Example	General topology
Turán graph	Example	Combinatorics
Two-element Boolean algebra	Example	Order, lattices, ordered algebraic structures
Circle as a quotient of the real line	Example	General topology
Cayley transform	Example	Functions of a complex variable
Forced oscillation and resonance	Example	Mechanics of particles and systems
Indiscrete topology	Example	General topology
Groups of order pq	Example	Group theory and generalizations
Seven Bridges of Königsberg	Example	Combinatorics
Harmonic oscillator	Example	Mechanics of particles and systems
Integers modulo n as a quotient group	Example	Group theory and generalizations
Determinant as a group homomorphism	Example	Linear and multilinear algebra; matrix theory
Baker's map	Example	Dynamical systems and ergodic theory
Regular open algebra	Example	Order, lattices, ordered algebraic structures
Warsaw circle	Example	General topology
Interval exchange transformation	Example	Dynamical systems and ergodic theory
Solenoid	Example	Topological groups, Lie groups
Non-standard model of arithmetic	Example	Mathematical logic and foundations
Unknot	Example	Manifolds and cell complexes
Beltrami–Klein model	Example	Geometry
Rotation group SO(3)	Example	Topological groups, Lie groups
Somos sequence	Example	Number theory
Ornstein–Zernike equation	Example	Statistical mechanics, structure of matter
Herbrand universe	Example	Mathematical logic and foundations
Category of groups	Example	Group theory and generalizations
Horocycle flow	Example	Dynamical systems and ergodic theory
Hilbert matrix	Example	Linear and multilinear algebra; matrix theory
Index of the de Rham complex	Example	Global analysis, analysis on manifolds
List of simple Lie groups	Example	Topological groups, Lie groups
Riemann zeta function as a series	Example	Sequences, series, summability
Space of convergent sequences c	Example	Functional analysis
Irrational rotation	Example	Dynamical systems and ergodic theory
Chinese restaurant process	Example	Probability theory and stochastic processes
Dense linear order	Example	Mathematical logic and foundations
Laplace transform of the Dirac delta	Example	Integral transforms, operational calculus
Cuntz algebra	Example	Functional analysis
A translation of the integers is not a homomorphism	Example	Group theory and generalizations
Joukowsky transform	Example	Functions of a complex variable
Hough transform	Example	Computer science
Lakes of Wada	Example	General topology
Weeks manifold	Example	Manifolds and cell complexes
Desargues configuration	Example	Combinatorics
Moulton plane	Example	Geometry
Baumslag–Solitar group	Example	Group theory and generalizations
Pseudosphere	Example	Differential geometry
Bilateral Laplace transform of a probability law	Example	Integral transforms, operational calculus
Minkowski question-mark function	Example	Real functions
Lagrange's theorem in S3	Example	Group theory and generalizations
Lamplighter group	Example	Group theory and generalizations
1 + 2 + 3 + 4 + ⋯	Example	Sequences, series, summability
Steiner quasigroup	Example	Group theory and generalizations
The integers modulo the even integers	Example	Group theory and generalizations
Mumford–Shah functional	Example	Calculus of variations and optimal control; optimization
Particular point topology	Example	General topology
Log-normal distribution	Example	Probability theory and stochastic processes
The special linear group is the kernel of the determinant	Example	Group theory and generalizations
Complex projective plane	Example	Geometry
Cross-polytope	Example	Convex and discrete geometry
Representation theory of SL2(R)	Example	Topological groups, Lie groups
Brieskorn manifold	Example	Several complex variables and analytic spaces
Involution as solution of Babbage's equation	Example	Difference and functional equations
Pareto distribution	Example	Probability theory and stochastic processes
Compact symplectic group	Example	Topological groups, Lie groups
Tropical semiring	Example	Associative rings and algebras
Geodesic flow on a locally symmetric space	Example	Dynamical systems and ergodic theory
Grandi's series	Example	Sequences, series, summability
Cantor group	Example	Topological groups, Lie groups
Symm's integral equation	Example	Potential theory
Skolem's paradox	Example	Mathematical logic and foundations
Shannon wavelet	Example	Harmonic analysis on Euclidean spaces
Category of rings	Example	Associative rings and algebras