Difference between revisions of "Converge"
Jump to navigation
Jump to search
(typo) |
|||
| Line 1: | Line 1: | ||
| − | In mathematics, a sequence <math> a_n</math> is generally said to '''converge''' to <math>x</math> if roughly speaking as <math> n </math> goes to infinity <math> a_n</math> gets closer and closer to <math>x</math> and stays there. | + | In mathematics, a sequence <math> a_n</math> is generally said to '''converge''' to <math>x</math> if roughly speaking as <math> n </math> goes to infinity <math> a_n</math> gets closer and closer to <math>x</math> and stays there. Rigorously, <math> a_n</math> is said to converge to <math>x</math> if for all <math>\epsilon>0</math> there exists </math> N</math> such that for all <math>n > N </math> we have <math>|a_n -x| < \epsilon </math>. |
Similar defintions can be made for convergence of functions. | Similar defintions can be made for convergence of functions. | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 00:24, March 14, 2007
In mathematics, a sequence <math> a_n</math> is generally said to converge to <math>x</math> if roughly speaking as <math> n </math> goes to infinity <math> a_n</math> gets closer and closer to <math>x</math> and stays there. Rigorously, <math> a_n</math> is said to converge to <math>x</math> if for all <math>\epsilon>0</math> there exists </math> N</math> such that for all <math>n > N </math> we have <math>|a_n -x| < \epsilon </math>.
Similar defintions can be made for convergence of functions.