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In mathematics, the ind-completion or ind-construction is the process of freely adding filtered colimits to a given category C. The objects in this ind-completed category, denoted Ind(C), are known as direct systems, they are functors from a small filtered category I to C. The dual concept is the pro-completion, Pro(C).
The term complete partial order, abbreviated cpo, has several possible meanings depending on context. A partially ordered set is a directed-complete partial order (dcpo) if each of its directed subsets has a supremum. (A subset of a partial order is directed if it is non-empty and every pair of elements has an upper bound in the subset.)
Matrix completion of a partially revealed 5 by 5 matrix with rank-1. Left: observed incomplete matrix; Right: matrix completion result. Matrix completion is the task of filling in the missing entries of a partially observed matrix, which is equivalent to performing data imputation in statistics. A wide range of datasets are naturally organized ...
In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset). The most familiar example is the completeness of the real numbers. A special use of the term refers to complete partial orders or complete lattices. However, many other interesting notions ...
In mathematics, specifically order theory, the Dedekind–MacNeille completion of a partially ordered set is the smallest complete lattice that contains it. It is named after Holbrook Mann MacNeille whose 1937 paper first defined and constructed it, and after Richard Dedekind because its construction generalizes the Dedekind cuts used by ...
An example is a tax return; filling one out is required in order for the amount of tax one owes to be determined. A form may also be a request for a tax refund. Forms may be filled out in duplicate (or triplicate, meaning three times) when the information gathered on the form needs to be distributed to several departments within an organisation.
Each transaction must succeed or fail as a complete unit; it can never be only partially complete. For example, when you purchase a book from an online bookstore, you exchange money (in the form of credit) for a book. If your credit is good, a series of related operations ensures that you get the book and the bookstore gets your money.
The source code comes with a 'complete.tcsh' file containing many examples of its completion syntax. Windows PowerShell , the extensible command shell from Microsoft, which is based on object-oriented programming and the Microsoft .NET framework, provides powerful and customizable completion capabilities similar to those of traditional Unix shells.