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In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way. The distinction between "canonical" and "normal ...
For example, the number of distinct anagrams of the word MISSISSIPPI is: 11 ! 1 ! 4 ! 4 ! 2 ! = 34650 {\displaystyle {\frac {11!}{1!\,4!\,4!\,2!}}=34650} . A k -permutation of a multiset M is a sequence of k elements of M in which each element appears a number of times less than or equal to its multiplicity in M (an element's repetition number ).
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more ...
Portal. v. t. e. In linguistics, syntax ( / ˈsɪntæks / SIN-taks) [1] [2] is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure ( constituency ), [3] agreement, the nature of crosslinguistic ...
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
Clipping (morphology) In linguistics, clipping, also called truncation or shortening, [1] is word formation by removing some segments of an existing word to create a synonym. [2] Clipping differs from abbreviation, which is based on a shortening of the written, rather than the spoken, form of an existing word or phrase.
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.
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 ...