Dedekind–MacNeille completion
（重定向自Dedekind completion）
![The Hasse diagram of a partially ordered set (left) and its Dedekind–MacNeille completion (right).](/Images/godic/202501/08/Dedekind-Macneille_completion.svg1839.png")
- "Dedekind completion" redirects here. For some other related concepts, see Dedekind completeness.
In order-theoretic mathematics, the Dedekind–MacNeille completion of a partially ordered set (also called the completion by cuts or normal completion) is the smallest complete lattice that contains the given partial order. 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 Dedekind to construct the real numbers from the rational numbers.