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:
“Your views are now my own.”
—Marvin Cohen, U.S. author and humorist.
In conversation, after having taken a strong position in an argument and heard a complete refutation of his position.
“The limerick packs laughs anatomical
Into space that is quite economical,
But the good ones I’ve seen
So seldom are clean
And the clean ones so seldom are comical.”
—Anonymous.