Difference between revisions of "Sequence"
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==Definition== | ==Definition== | ||
| − | A sequence of real numbers is simply a function <math>f : \mathbb{N} \rightarrow \mathbb{R}</math>. For instance, the function <math>f(x) = x^2</math> corresponds to the sequence <math>X = (x_n) = (0, 1, 4, 9, 16, \ldots)</math>. | + | A sequence of real numbers is simply a function <math>f : \mathbb{N} \rightarrow \mathbb{R}</math>. For instance, the function <math>f(x) = x^2</math> defined on <math>\mathbb{N}</math> corresponds to the sequence <math>X = (x_n) = (0, 1, 4, 9, 16, \ldots)</math>. |
==Convergence== | ==Convergence== | ||
Revision as of 12:55, 18 May 2008
A sequence is an ordered list of terms. Sequences may be either finite or infinite.
Contents
Definition
A sequence of real numbers is simply a function 
. For instance, the function 
defined on 
corresponds to the sequence 
.
Convergence
Let 
be a sequence of reals. converges to 
if and only if for all positive reals 
, there exists a positive integer 
such that for all integers 
, we have 
. If converges to 
, is called the limit of and is written 
.
Resources
- Online Encyclopedia of Integer Sequences -- A really cool math tool.
See Also
This article is a stub. Help us out by expanding it.
