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.