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Finagle's law of dynamic negatives (also known as Melody's law, Sod's Law or Finagle's corollary to Murphy's law) is usually rendered as "Anything that can go wrong, will—at the worst possible moment." The term "Finagle's law" was first used by John W. Campbell Jr., the influential editor of Astounding Science Fiction (later Analog).
This definition of exponentiation with negative exponents is the only one that allows extending the identity + = to negative exponents (consider the case =). The same definition applies to invertible elements in a multiplicative monoid , that is, an algebraic structure , with an associative multiplication and a multiplicative identity denoted 1 ...
Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same.
For example, there may be 1 ⁄ 4 as many authors publishing two articles within a specified time period as there are single-publication authors, 1 ⁄ 9 as many publishing three articles, 1 ⁄ 16 as many publishing four articles, etc. Though the law itself covers many disciplines, the actual ratios involved are very discipline-specific.
Engineering notation or engineering form (also technical notation) is a version of scientific notation in which the exponent of ten is always selected to be divisible by three to match the common metric prefixes, i.e. scientific notation that aligns with powers of a thousand, for example, 531×10 3 instead of 5.31×10 5 (but on calculator displays written without the ×10 to save space).
The sequence of powers of ten can also be extended to negative powers. Similar to the positive powers, the negative power of 10 related to a short scale name can be determined based on its Latin name-prefix using the following formula: 10 −[(prefix-number + 1) × 3] Examples: billionth = 10 −[(2 + 1) × 3] = 10 −9
In calculus, the reciprocal rule gives the derivative of the reciprocal of a function f in terms of the derivative of f.The reciprocal rule can be used to show that the power rule holds for negative exponents if it has already been established for positive exponents.
In 2017, it was proven [15] that there exists a unique function F which is a solution of the equation F(z + 1) = exp(F(z)) and satisfies the additional conditions that F(0) = 1 and F(z) approaches the fixed points of the logarithm (roughly 0.318 ± 1.337i) as z approaches ±i∞ and that F is holomorphic in the whole complex z-plane, except the ...
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