Sequences, series, summability Sequences and limits Concept
Limit of a sequence
Summary
A sequence has a limit when its terms come and stay arbitrarily close to for large indices. Limits of sequences are the base of the notions of convergence, continuity and series in analysis. The node limit of a sequence gives the precise definition.
Where this leads
24 pages build on this one.
- Truncation error
- Gelfand's formula
- Kingman's subadditive ergodic theorem
- Fekete's lemma
- Root-finding algorithm
- Singular integral operator
- Continuous functional calculus
- Natural density
- Arithmetic–geometric mean and elliptic integrals
- Weyl's criterion
- Continuity of measure from below and above
- Lie product formula
- Numerical analysis
- Spectral radius formula
- Oseledets theorem
- Commutative Gelfand–Naimark theorem
- Equidistribution modulo one
- Noncommutative geometry
- Rate of convergence
- Gelfand's spectral radius formula
- Pesin theory
- Asymptotic stability of linear recurrences
- Chebyshev constant
- Golden–Thompson inequality
Further reading
- Web https://en.wikipedia.org/wiki/Limit_of_a_sequence, lead section
About this page
| Tag | 05M5SWSZZD |
|---|---|
| URI | m2://05M5SWSZZD |
| Kind | concept |
| Writing | W1 stated |
| MSC | 40A05 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Truncation error
- Gelfand's formula
- Fekete's lemma
- Root-finding algorithm
- Singular integral operator
- Natural density
- Arithmetic–geometric mean and elliptic integrals
- Continuity of measure from below and above
- Lie product formula
- Numerical analysis
- Equidistribution modulo one
- Rate of convergence
- Gelfand's spectral radius formula
- Asymptotic stability of linear recurrences