Sequence

Definition

In mathematics, a sequence is a collection of objects possibly with repetition, that come in a specified order. Like a set, it contains members. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. The notion of a sequence can be generalized to an indexed family, defined as a function from an arbitrary index set.

Related concepts

1/2 + 1/4 + 1/8 + 1/16 + ⋯1/2 − 1/4 + 1/8 − 1/16 + ⋯1/4 + 1/16 + 1/64 + 1/256 + ⋯1 + 1 + 1 + 1 + ⋯1 + 2 + 3 + 4 + ⋯1 + 2 + 4 + 8 + ⋯1 − 1 + 2 − 6 + 24 − 120 + ⋯1 − 2 + 3 − 4 + ⋯1 − 2 + 4 − 8 + ⋯Absolute convergence Algebraic function Algebraic structure Algebraic topology Alphabet (computer science)Alternating series Analysis (mathematics)Analytic function Arithmetic progression Automatic sequence Base 2 Bijection Binary relation Binary sequence Binet's formula Bit Boolean-valued function Boolean function Cantor's diagonal argument Cantor space Cartesian product Cauchy product Cauchy sequence Character (computing)Coarsest topology Codomain Compact space Complete metric space Complete sequence Completeness of the real numbers Complex-valued function Complex conjugate Complex number Computer memory Computer science Computing Conditional convergence Connected space Constant-recursive sequence Constant (mathematics)Constant function Continuous (topology)Continuous function Convergent series Coprime Counting measure Cube (algebra)Decimal expansion Differential equations Dirichlet series Discrete-time signal Divergence of the sum of the reciprocals of the primes Divergent series Divisor Domain of a function Element (mathematics)Ellipsis Encyclopedia of Mathematics Enumeration European Mathematical Society Even integer Exact sequence FK-space Factorial Farey sequence Fibonacci number Fibonacci sequence Field (mathematics)Figurate number Filter on a set Finite set Finiteness Formal language Formal power series Fourier series Free monoid Free semigroup Fréchet space Function (mathematics)Function composition Function of a complex variable Function of a real variable Function of several complex variables Function of several real variables Function space Functor Generalized hypergeometric series Generating series Geometric progression Grandi's series Group (mathematics)Group homomorphism Group theory Harmonic progression (mathematics)Harmonic series (mathematics)Heptagonal number Hexagonal number Higher-order function History of the function concept Holonomic function Holonomic sequence Homological algebra Homotopy theory Hypergeometric function Hypergeometric function of a matrix argument Identity function Image (mathematics)Implicit function Index set Indexed family Infinite arithmetic series Injective function Integer Integer-valued function Integer sequence Integers Interval (mathematics)Inverse function Irrational number James R. Munkres Jean Leray K-regular sequence Kernel (algebra)Kleene star Lambda calculus Large enough Laurent series Lauricella hypergeometric series Limit of a sequence Limit ordinal Linear map Linear recurrence Linear subspace List (computer science)List (computing)List of OEIS sequences List of integer sequences List of mathematical functions List of mathematical series Look-and-say sequence Lp space Lucas number Mathematical analysis Mathematical object Mathematics Measurable function Metric (mathematics)Metric space Metric spaces Modular hypergeometric series Module (mathematics)Module homomorphism Modulus of complex number Monoid Monomial basis Monotonic function Morphism Multivalued function N-tuple Natural logarithm Natural number Natural numbers Natural topology Neil Sloane Net (mathematics)Net (topology)Norm (mathematics)Number theory Numerical digit On-Line Encyclopedia of Integer Sequences Order topology Ordered pair Partial function Pell number Pentagonal number Periodic sequence Permutation Pi Pointwise addition Pointwise convergence Polygonal number Polynomial Polynomial sequence Power of 10 Power of three Power of two Power series Prime number Product space Product topology Projection (set theory)Pseudorandom binary sequence Puiseux series Random sequence Range of a function Rational function Rational number Rational numbers Real-valued function Real analysis Real number Recamán's sequence Recurrence relation Recursion (computer science)Recursive definition Relation (mathematics)Restriction (mathematics)Riemann's differential equation Riemann zeta function Separable space Sequence (disambiguation)Sequence space Sequential (disambiguation)Sequential compactness Series (mathematics)Set-valued function Set (mathematics)Shortlex order Smooth function Space (mathematics)Special functions Spectral sequence Square number Squeeze theorem Stream (computer science)Stream (computing)String (computer science)Subsequence Surjective function Taylor series Telescoping series Tessellation Theoretical computer science Theta hypergeometric series Thue–Morse sequence Topological space Topological vector space Topology Triangular array Triangular number Trigonometric series Tuple Uniform convergence Vector (geometric)Vector space Word (formal language theory)±1-sequence Ω-language

25 concepts already in your glossary