Cauchy sequences Limit of a sequence

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the plot of cauchy sequence (xn), shown in blue, xn versus n. visually, see sequence appears converging limit point terms in sequence become closer n increases. in real numbers every cauchy sequence converges limit.


a cauchy sequence sequence terms become arbitrarily close together, after sufficiently many initial terms have been discarded. notion of cauchy sequence important in study of sequences in metric spaces, and, in particular, in real analysis. 1 particularly important result in real analysis cauchy criterion convergence of sequences: sequence of real numbers convergent if , if cauchy sequence. remains true in other complete metric spaces.







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