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Strict weak orders are very closely related to total preorders or (non-strict) weak orders, and the same mathematical concepts that can be modeled with strict weak orderings can be modeled equally well with total preorders. A total preorder or weak order is a preorder in which any two elements are comparable. [7]
The 13 possible strict weak orderings on a set of three elements {a, b, c} In number theory and enumerative combinatorics, the ordered Bell numbers or Fubini numbers count the weak orderings on a set of elements. Weak orderings arrange their elements into a sequence allowing ties, such as might arise as the outcome of a horse race. [1] [2]
"Ordered" means that the elements of the data type have some kind of explicit order to them, where an element can be considered "before" or "after" another element. This order is usually determined by the order in which the elements are added to the structure, but the elements can be rearranged in some contexts, such as sorting a list. For a ...
Merge sort. In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order.The most frequently used orders are numerical order and lexicographical order, and either ascending or descending.
In C++, any class that can be three-way compared can be a parameter to instances of std::compare_three_way, std::strong_order, std::weak_order, or std::partial_order. Since Java version 1.5, the same can be computed using the Math.signum static method if the difference can be known without computational problems such as arithmetic overflow ...
In computer science, a list or sequence is a collection of items that are finite in number and in a particular order. An instance of a list is a computer representation of the mathematical concept of a tuple or finite sequence. A list may contain the same value more than once, and each occurrence is considered a distinct item.
In computer science, one can find examples of the following preorders. Asymptotic order causes a preorder over functions :. The corresponding equivalence relation is called asymptotic equivalence. Polynomial-time, many-one (mapping) and Turing reductions are preorders on complexity classes.
In mathematics, specifically in order theory and functional analysis, an element of a vector lattice is called a weak order unit in if and also for all , {, | |} = = [1] Examples [ edit ]