Difference between revisions of "Converge"
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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>. | 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 | + | Similar definitions can be made for convergence of functions. |
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 00:25, 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 definitions can be made for convergence of functions.