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The N = 2 superconformal algebra is the Lie superalgebra with basis of even elements c, L n, J n, for n an integer, and odd elements G + r, G − r, where (for the Ramond basis) or + (for the Neveu–Schwarz basis) defined by the following relations: [1]
In mathematics, the Bernoulli numbers B n are a sequence of rational numbers which occur frequently in analysis.The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain ...
Given real numbers x and y, integers m and n and the set of integers, floor and ceiling may be defined by the equations ⌊ ⌋ = {}, ⌈ ⌉ = {}. Since there is exactly one integer in a half-open interval of length one, for any real number x, there are unique integers m and n satisfying the equation
The term algebra is derived from the Arabic word al-jabr meaning 'the reunion of broken parts' that he used for naming one of these methods in the title of his main treatise. [31] [32] Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified ...
With this definition, given a natural number n, the sentence "a set S has n elements" can be formally defined as "there exists a bijection from n to S." This formalizes the operation of counting the elements of S. Also, n ≤ m if and only if n is a subset of m. In other words, the set inclusion defines the usual total order on the natural numbers.
Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein's formula = is the quantitative representation in mathematical notation of mass–energy equivalence. [1]