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A number that is not part of any friendly pair is called solitary. The abundancy index of n is the rational number σ(n) / n, in which σ denotes the sum of divisors function. A number n is a friendly number if there exists m ≠ n such that σ(m) / m = σ(n) / n. Abundancy is not the same as abundance, which is defined as σ(n) − 2n.
Dunbar's number has become of interest in anthropology, evolutionary psychology, [12] statistics, and business management.For example, developers of social software are interested in it, as they need to know the size of social networks their software needs to take into account; and in the modern military, operational psychologists seek such data to support or refute policies related to ...
Also included are groups in arts and entertainment (both fictional characters and performers or artists) and in history, and groups of abstract concepts. Criteria for inclusion: In order to be included in these lists, a group should be well known as a group, rather than being loosely associated people or concepts which happen to total to the ...
In group theory, a branch of mathematics, an opposite group is a way to construct a group from another group that allows one to define right action as a special case of left action. Monoids , groups, rings , and algebras can be viewed as categories with a single object.
The monster group contains 20 sporadic groups (including itself) as subquotients. Robert Griess, who proved the existence of the monster in 1982, has called those 20 groups the happy family, and the remaining six exceptions pariahs. It is difficult to give a good constructive definition of the monster because of its complexity.
Thus the group-theoretic notion of commensurability generalizes the concept for real numbers. There is a similar notion for two groups which are not given as subgroups of the same group. Two groups G 1 and G 2 are (abstractly) commensurable if there are subgroups H 1 ⊂ G 1 and H 2 ⊂ G 2 of finite index such that H 1 is isomorphic to H 2.
But if it is used only on the left, it groups two or more simultaneous equations. There are other symbols of grouping. One is the bar above an expression, as in the square root sign in which the bar is a symbol of grouping. For example √ p+q is the square root of the sum. The bar is also a symbol of grouping in repeated decimal digits.
An antonym is one of a pair of words with opposite meanings. Each word in the pair is the antithesis of the other. A word may have more than one antonym. There are three categories of antonyms identified by the nature of the relationship between the opposed meanings.