Top definition

by Dongo February 07, 2006

2

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.

by Subsequence February 16, 2010

3

by sylvy September 24, 2006