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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 ...
Order of operations. In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression . These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and ...
Definition. The words in a lexicon (the set of words used in some language) have a conventional ordering, used in dictionaries and encyclopedias, that depends on the underlying ordering of the alphabet of symbols used to build the words. The lexicographical order is one way of formalizing word order given the order of the underlying symbols.
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.
Formal proof. In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language ), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. It differs from a natural language argument in that it ...
Group (mathematics) The manipulations of the Rubik's Cube form the Rubik's Cube group. In mathematics, a group is a set with an operation that satisfies the following constraints: the operation is associative and has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with ...