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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. Rigoroulsy 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>.