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In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The word partial is used to indicate that not every pair of elements needs to be comparable; that is, there may be pairs for which neither element precedes the other.
Class (set theory) In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. Classes act as a way to have set-like collections while differing from sets so as to avoid paradoxes, especially ...
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, n th, etc.) aimed to extend enumeration to infinite sets. [1] A finite set can be enumerated by successively labeling each element with the least natural number that has not been previously used.
Order theory. Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions.
Bag-of-words model. The bag-of-words model is a model of text which uses a representation of text that is based on an unordered collection (or "bag") of words. It is used in natural language processing and information retrieval (IR). It disregards word order (and thus any non-trivial notion of grammar [clarification needed]) but captures ...
Mathematical structure. In mathematics, a structure is a set provided with some additional features on the set (e.g. an operation, relation, metric, or topology ). Often, the additional features are attached or related to the set, so as to provide it with some additional meaning or significance. A partial list of possible structures are ...
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element a ...
v. t. e. In linguistics, word order (also known as linear order) is the order of the syntactic constituents of a language. Word order typology studies it from a cross-linguistic perspective, and examines how languages employ different orders. Correlations between orders found in different syntactic sub-domains are also of interest.