Difference between revisions of "Converge"

Revision as of 00:25, March 14, 2007

In mathematics, a sequence $a_{n}$ is generally said to converge to $x$ if roughly speaking as $n$ goes to infinity $a_{n}$ gets closer and closer to $x$ and stays there. Rigorously, $a_{n}$ is said to converge to $x$ if for all $\epsilon >0$ there exists $N$ such that for all $n>N$ we have $|a_{n}-x|<\epsilon$ .

Similar definitions can be made for convergence of functions.

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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 definitions can be made for convergence of functions.
 [[Category:Mathematics]]

Difference between revisions of "Converge"

Revision as of 00:25, March 14, 2007

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