different between preorder vs precongruence
preorder
English
Etymology
pre- +? order.
Verb
preorder (third-person singular simple present preorders, present participle preordering, simple past and past participle preordered)
- (transitive) To order (goods or services) in advance, before they are available.
- (transitive) To sort or arrange beforehand.
Translations
Noun
preorder (plural preorders)
- An order for goods or services placed in advance.
- (set theory, order theory) A binary relation that is reflexive and transitive.
- 2002, Yves Nievergelt, Foundations of Logic and Mathematics, Springer (Birkhäuser), page 152,
- Example 436 For each set , the relation is a preorder on .
- 2010, S. Kaci, Refined Preference-Based Argumentation Frameworks, Pietro Baroni, F. Cerutti, M. Giacomin, G. R. Simari (editors), Computational Models of Argument: Proceedings of COMMA 2010, IOS Press, page 306,
- Let us first compare , and w.r.t. the partial preorder .
- 2000, Jean-Charles Pomerol, Sergio Barba-Romero, Multicriterion Decision in Management: Principles and Practice, Springer, Softcover, page 58,
- It can easily be verified that the above relation is a preorder, i.e. that it is reflexive and transitive.
- 2002, Yves Nievergelt, Foundations of Logic and Mathematics, Springer (Birkhäuser), page 152,
Synonyms
- (binary relation that is reflexive and transitive): quasiorder
Hyponyms
- (binary relation that is reflexive and transitive):
- partial order
- total order
- well-order
- total order
- partial order
Derived terms
- preorder algebra
- preorder atom
- preorder functor
- strict preorder
Related terms
- preordered set
Translations
Adjective
preorder (not comparable)
- (computing theory, of a traversal of a tree) Such that, recursively, the root is visited before the left and right subtrees.
- 2002, Gabriel Valiente, Algorithms on Trees and Graphs, Springer, page 115,
- Now, the preorder traversal of a tree can be constructed from the preorder traversals of the subtrees rooted at the children of the root of the tree.
- 2006, ISRD Group, Data Structures Using C, Tata McGraw-Hill Education, page 254,
- In the program given above, tree is constructed and is traversed in inorder, preorder and postorder traversal.
- 2011, Ananda Rao Akepogu, Radhika Raju Palagiri, Data Structures and Algorithms Using C++, Pearson Education India, page 9.16,
- The preorder traversal visits a node first after which it traverses its left subtree and then traverses its right subtree.
- 2002, Gabriel Valiente, Algorithms on Trees and Graphs, Springer, page 115,
Coordinate terms
- inorder
- postorder
Hypernyms
- depth-first
preorder From the web:
- what pre order means
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precongruence
English
Etymology
pre- +? congruence
Noun
precongruence (plural precongruences)
- (mathematics) A congruence of a preorder
precongruence From the web:
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