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The converse of this implication leads to functions that are order-reflecting, i.e. functions f as above for which f(a) ≤ f(b) implies a ≤ b. On the other hand, a function may also be order-reversing or antitone, if a ≤ b implies f(a) ≥ f(b). An order-embedding is a function f between orders that is both order-preserving and order ...
The nested set model is a technique for representing nested set collections (also known as trees or hierarchies) in relational databases.. It is based on Nested Intervals, that "are immune to hierarchy reorganization problem, and allow answering ancestor path hierarchical queries algorithmically — without accessing the stored hierarchy relation".
RedBeanPHP is the first library known to adopt the on-the-fly approach towards ORM. As such it has a big influence on other libraries. RedBeanPHP inspired many other projects to embrace this approach towards object mapping. Similar libraries have appeared for .NET, [1] Python, [2] JavaScript, [3] Java, [4] Erlang, [5] ColdFusion [6] and ...
A prefix order is a binary relation "≤" over a set P which is antisymmetric, transitive, reflexive, and downward total, i.e., for all a, b, and c in P, we have that: a ≤ a (reflexivity); if a ≤ b and b ≤ a then a = b (antisymmetry); if a ≤ b and b ≤ c then a ≤ c (transitivity); if a ≤ c and b ≤ c then a ≤ b or b ≤ a ...
A base relation representing this kind of entity is called, informally, an associative table. An associative entity (using Chen notation) As mentioned above, associative entities are implemented in a database structure using associative tables, which are tables that can contain references to columns from the same or different database tables ...
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
Object–relational mapping (ORM, O/RM, and O/R mapping tool) in computer science is a programming technique for converting data between a relational database and the memory (usually the heap) of an object-oriented programming language.
The incomparability relation is always symmetric and it will be reflexive if and only if < is an irreflexive relation (which is assumed by the above definition). Consequently, a strict partial order < is a strict weak order if and only if its induced incomparability relation is an equivalence relation.