Difference between revisions of "Limit of a sequence"

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(Created page with "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 conve...")
 
(See also)
 
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== Description ==
 
== Description ==
  
If such a limit exists, the sequence is called convergent.
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If such a limit exists, the sequence is called '''convergent'''.
  
A sequence which does not converge is said to be divergent.
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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.
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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 ==
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* [[Convergence of random variables]]
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* [[Limit of a function]]
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* Limit of a net - see [[Net (mathematics)]], a topological generalization of a sequence.
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* [[Mathematical analysis]]
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* [[Modes of convergence]]
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* [[Shift rule]]
  
 
== External links ==
 
== External links ==

Latest revision as of 19:19, 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

External links