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In mathematical analysis, a metric space M is complete provided every Cauchy sequence of points in M converges to a point in M.

R^n, the set of n-tuples of real numbers, and l_2, the set of square-summable sequences, are complete.

Q, the set of all rational numbers, is not complete. For example, the sequence

3, 3.1, 3.14, 3.141, 3.1415, 3.14159...

where each term is a further approximation to pi, is Cauchy in Q but does not converge to a rational number.

Q, the set of all rational numbers, is not complete. For example, the sequence

3, 3.1, 3.14, 3.141, 3.1415, 3.14159...

where each term is a further approximation to pi, is Cauchy in Q but does not converge to a rational number.

de Subsequence
16 Februarie 2010