Difference between revisions of "Sequence"
m (→Definition) |
|||
Line 2: | Line 2: | ||
==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 11:55, 18 May 2008
A sequence is an ordered list of terms. Sequences may be either finite or infinite.
Contents
[hide]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.