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:
“In Stamps the segregation was so complete that most Black children didn’t really, absolutely know what whites looked like.”
—Maya Angelou (b. 1928)
“The woman’s world ... is shown as a series of limited spaces, with the woman struggling to get free of them. The struggle is what the film is about; what is struggled against is the limited space itself. Consequently, to make its point, the film has to deny itself and suggest it was the struggle that was wrong, not the space.”
—Jeanine Basinger (b. 1936)