Complete Metric Space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M.
Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary). For instance, the set of rational numbers is not complete, because e.g. is "missing" from it, even though one can construct a Cauchy sequence of rational numbers that converges to it. (See the examples below.) It is always possible to "fill all the holes", leading to the completion of a given space, as explained below.
Read more about Complete Metric Space: Examples, Some Theorems, Completion, Topologically Complete Spaces, Alternatives and Generalizations
Famous quotes containing the words complete and/or space:
“Better wear out shoes than sheets.”
—18th-century Scottish proverb, collected in J. Kelly, Complete Collection of Scottish Proverbs (1721)
“Play is a major avenue for learning to manage anxiety. It gives the child a safe space where she can experiment at will, suspending the rules and constraints of physical and social reality. In play, the child becomes master rather than subject.... Play allows the child to transcend passivity and to become the active doer of what happens around her.”
—Alicia F. Lieberman (20th century)