Difference between revisions of "Limit of a sequence"
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== Description == | == Description == | ||
| − | If such a limit exists, the sequence is called convergent. | + | If such a limit exists, the sequence is called '''convergent'''. |
| − | A sequence which does not converge is said to be divergent. | + | A sequence which does not converge is said to be '''divergent'''. |
| − | The limit of a sequence is said to be the fundamental notion on which the whole of analysis ultimately rests. | + | The limit of a sequence is said to be the fundamental notion on which the whole of [[mathematical analysis]] ultimately rests. |
Limits can be defined in any metric or topological space, but are usually first encountered in the [[Real number|real numbers]]. | Limits can be defined in any metric or topological space, but are usually first encountered in the [[Real number|real numbers]]. | ||
== See also == | == See also == | ||
| + | |||
| + | * [[Convergence of random variables]] | ||
| + | * [[Limit of a function]] | ||
| + | * Limit of a net - see [[Net (mathematics)]], a topological generalization of a sequence. | ||
| + | * [[Mathematical analysis]] | ||
| + | * [[Modes of convergence]] | ||
| + | * [[Shift rule]] | ||
== External links == | == External links == | ||
Latest revision as of 20:19, 18 September 2016
In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to".
Description
If such a limit exists, the sequence is called convergent.
A sequence which does not converge is said to be divergent.
The limit of a sequence is said to be the fundamental notion on which the whole of mathematical analysis ultimately rests.
Limits can be defined in any metric or topological space, but are usually first encountered in the real numbers.
See also
- Convergence of random variables
- Limit of a function
- Limit of a net - see Net (mathematics), a topological generalization of a sequence.
- Mathematical analysis
- Modes of convergence
- Shift rule
External links
- Limit of a sequence @ Wikipedia.org
