Difference between revisions of "Converge"
From Conservapedia
(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 
is generally said to converge to 
if roughly speaking as 
goes to infinity gets closer and closer to and stays there. Rigorously, is said to converge to if for all 
there exists </math> N</math> such that for all 
we have 
.
Similar defintions can be made for convergence of functions.
