Converge - Revision history

DavidB4-bot: /* top */Spelling, Grammar, and General Cleanup

2016-06-30T18:37:11Z

top: Spelling, Grammar, and General Cleanup

2008-09-12T20:13:17Z

wikify

2007-04-01T16:58:16Z

2007-03-22T22:38:20Z

2007-03-14T00:26:50Z

math tags currently broken, so took n > N out of math until fixed.

2007-03-14T00:26:18Z

math tags currently broken, so took n > N out of math until fixed.

2007-03-14T00:25:40Z

typo typo

2007-03-14T00:25:25Z

typo again

2007-03-14T00:24:51Z

typo

2007-03-11T10:33:41Z

← Older revision		Revision as of 18:37, June 30, 2016
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	Similar definitions can be made for convergence of [[function]]s.		Similar definitions can be made for convergence of [[function]]s.

−	[[~~category~~: Topology]]	+	[[Category:Topology]]

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-In a [[metric space]] (X, d), a sequence <math> a_n</math> in X is said to '''converge''' to a point <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 N such that for all n > N we have <math>d\left (a_n, x\right ) < \epsilon </math>.
+In a [[metric space]] (X, d), a [[sequence]] <math> a_n</math> in X is said to '''converge''' to a point <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 N such that for all n > N we have <math>d\left (a_n, x\right ) < \epsilon </math>.
-Similar definitions can be made for convergence of functions.
+Similar definitions can be made for convergence of [[function]]s.
 [[category: Topology]]

@@ 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.  Rigorously, <math> a_n</math> is said to converge to <math>x</math> if for all <math>\epsilon>0</math> there exists N such that for all n > N we have <math>|a_n -x| < \epsilon </math>.
+In a [[metric space]] (X, d), a sequence <math> a_n</math> in X is said to '''converge''' to a point <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 N such that for all n > N we have <math>d\left (a_n, x\right ) < \epsilon </math>.
 Similar definitions can be made for convergence of functions.
 [[Category:Mathematics]]

@@ 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.  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 n > N 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 N such that for all n > N we have <math>|a_n -x| < \epsilon </math>.
 Similar definitions can be made for convergence of functions.
 [[Category:Mathematics]]

@@ 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. Rigoroulsy, <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 defintions can be made for convergence of functions.
 [[Category:Mathematics]]

← Older revision		Revision as of 10:33, March 11, 2007
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	Similar defintions can be made for convergence of functions.		Similar defintions can be made for convergence of functions.
		+
		+	[[Category:Mathematics]]