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The zigzag numbers in Bernoulli (1742), Opera Omnia vol. 4, p. 105. The determination of the number A n of alternating permutations of the set {1, ..., n} is called André's problem. The numbers A n are variously known as Euler numbers, zigzag numbers, up/down numbers, or by some combinations of these names.
In mathematics, an alternating group is the group of even permutations of a finite set. The alternating group on a set of n elements is called the alternating group of degree n , or the alternating group on n letters and denoted by A n or Alt( n ).
A form of unary notation called Church encoding is used to represent numbers within lambda calculus. Some email spam filters tag messages with a number of asterisks in an e-mail header such as X-Spam-Bar or X-SPAM-LEVEL. The larger the number, the more likely the email is considered spam. 10: Bijective base-10: To avoid zero: 26: Bijective base-26
In mathematics, the harmonic series ... Another proof that the harmonic numbers are ... is known as the alternating harmonic series. It is conditionally convergent by ...
R – real numbers. ran – range of a function. rank – rank of a matrix. (Also written as rk.) Re – real part of a complex number. [2] (Also written.) resp – respectively. RHS – right-hand side of an equation. rk – rank. (Also written as rank.) RMS, rms – root mean square. rng – non-unital ring. rot – rotor of a vector field.
In mathematics, an alternating series is an infinite series of terms that alternate between positive and negative signs. In capital-sigma notation this is expressed ∑ n = 0 ∞ ( − 1 ) n a n {\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}} or ∑ n = 0 ∞ ( − 1 ) n + 1 a n {\displaystyle \sum _{n=0}^{\infty }(-1)^{n+1}a_{n}} with a n ...
Alternative algebras are so named because they are the algebras for which the associator is alternating.The associator is a trilinear map given by [,,] = ().By definition, a multilinear map is alternating if it vanishes whenever two of its arguments are equal.
The threefold Cauchy product of 1 − 1 + 1 − 1 + ... is 1 − 3 + 6 − 10 + ..., the alternating series of triangular numbers; its Abel and Euler sum is 1 ⁄ 8. [16] The fourfold Cauchy product of 1 − 1 + 1 − 1 + ... is 1 − 4 + 10 − 20 + ..., the alternating series of tetrahedral numbers , whose Abel sum is 1 ⁄ 16 .
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