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A problem related to the order-maintenance problem is the list-labeling problem in which instead of the order(X, Y) operation the solution must maintain an assignment of labels from a universe of integers {,, …,} to the elements of the set such that X precedes Y in the total order if and only if X is assigned a lesser label than Y.
A partially ordered set (poset for short) is an ordered pair = (,) consisting of a set (called the ground set of ) and a partial order on . When the meaning is clear from context and there is no ambiguity about the partial order, the set X {\displaystyle X} itself is sometimes called a poset.
In Political science and Decision theory, order relations are typically used in the context of an agent's choice, for example the preferences of a voter over several political candidates. x ≺ y means that the voter prefers candidate y over candidate x. x ~ y means the voter is indifferent between candidates x and y.
C program source text is free-form code. Semicolons terminate statements, while curly braces are used to group statements into blocks. The C language also exhibits the following characteristics: The language has a small, fixed number of keywords, including a full set of control flow primitives: if/else, for, do/while, while, and switch.
In discrete optimization, a special ordered set (SOS) is an ordered set of variables used as an additional way to specify integrality conditions in an optimization model. . Special order sets are basically a device or tool used in branch and bound methods for branching on sets of variables, rather than individual variables, as in ordinary mixed integer programm
A set equipped with a total order is a totally ordered set; [5] the terms simply ordered set, [2] linearly ordered set, [3] [5] toset [6] and loset [7] [8] are also used. The term chain is sometimes defined as a synonym of totally ordered set , [ 5 ] but generally refers to a totally ordered subset of a given partially ordered set.
If the semantics of the program language restrict the compiler into translating the expression in left-to-right order (for example), then the generated code will look as if the programmer had written the following statements in the original program: sum = a + b; sum = sum + c;
Partially ordered class and totally ordered class are defined in a similar way. These concepts generalize respectively those of preordered set, partially ordered set and totally ordered set. However, it is difficult to work with them as in the small case because many constructions common in a set theory are no longer possible in this framework.