mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though Knuth's...
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fifth hyperoperation. Pentation is defined to be repeated tetration, similarly to how tetration is repeated exponentiation, exponentiation is repeated multiplication...
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Reuben Goodstein after the Greek prefix of n suffixed with -ation (such as tetration (n = 4), pentation (n = 5), hexation (n = 6), etc.) and can be written...
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Knuth's up-arrow notation (section Using tetration)
now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation, etc., for the extended operations beyond exponentiation. The...
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the function f ( x ) = x x . {\displaystyle f(x)=x^{x}.} The infinite tetration x x x ⋅ ⋅ ⋅ {\displaystyle x^{x^{x^{\cdot ^{\cdot ^{\cdot }}}}}} or ∞...
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which makes it a power of two. 256 is 4 raised to the 4th power, so in tetration notation, 256 is 24. 256 is the value of the expression n n {\displaystyle...
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exponentiation; this operation is sometimes called hyper-4 or tetration. Iterating tetration leads to another operation, and so on, a concept named hyperoperation...
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of two are common. The first 20 of them are: Also see Fermat number, tetration and lower hyperoperations. All of these numbers over 4 end with the digit...
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= 2 × 2 {\displaystyle 2^{2}=2\times 2} . It is also equal to 32 (see tetration). The aliquot sum of 16 is 15, within an aliquot sequence of four composite...
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multiple up arrows, such as ⇈, for iterated, or repeated, exponentiation (tetration). The quantum theory of electron spin uses either upward or downward arrows...
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\uparrow 2\uparrow \uparrow (3+2\uparrow \uparrow 8),} which contains three tetrations. In 2019 this was further improved to: N ″ = ( 2 ↑↑ 5138 ) ⋅ ( ( 2 ↑↑...
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by which the magnitude of a googolplex could be represented, such as tetration, hyperoperation, Knuth's up-arrow notation, Steinhaus–Moser notation,...
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hyperoperations, used to build addition, multiplication, exponentiation, tetration, etc. It was studied in 1986 in an investigation involving generalization...
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the set of real or rational numbers, is not commutative or associative. Tetration ( ↑↑ {\displaystyle \uparrow \uparrow } ), as a binary operation on the...
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Mobile collaboration and cloud computing United States — February 2014 Tetration Analytics Data Center Analytics and Security Solution United States —...
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{e^{e^{\cdot ^{\cdot ^{e}}}}} _{k\ e'{\text{s}}}=e\uparrow \uparrow k} using tetration or Knuth's up-arrow notation. To see the divergence of the series (4)...
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in the OEIS). 65536 is 2 2 2 2 {\displaystyle 2^{2^{2^{2}}}} , so in tetration notation 65536 is 42. When expressed using Knuth's up-arrow notation,...
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number, larger than what can be represented even using power towers (tetration). However, it can be represented using layers of Knuth's up-arrow notation...
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Wiktionary, the free dictionary. ^^ may refer to: A kaomoji Tetration, the ASCII form of the tetration operator Record separator, control character in the caret...
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logit. They are the inverse functions of the double exponential function, tetration, of f(w) = wew, and of the logistic function, respectively. From the perspective...
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in minor details of rounding) and forms an inverse to the operation of tetration. The iterated logarithm is useful in analysis of algorithms and computational...
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H-function Hyper operators Iterated logarithm Pentation Super-logarithms Tetration Lambert W function: Inverse of f(w) = w exp(w). Lamé function Mathieu...
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Hyperexponential can refer to: The hyperexponential distribution in probability. Tetration, also known as hyperexponentiation. This disambiguation page lists articles...
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} This sum is transcendental because it is a Liouville number. Like tetration, there is currently no accepted method of extension of the exponential...
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more classes of growth behavior, like the hyperoperations beginning at tetration, and A ( n , n ) {\displaystyle A(n,n)} , the diagonal of the Ackermann...
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number is too large to reasonably express using exponentiation or even tetration. For more about modern usage for large numbers, see Large numbers. To...
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introduced by Hans Maurer (1901) and Reuben Louis Goodstein (1947) for tetration, or with David Patterson Ellerman's (1995) nx pre-superscript notation...
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mechanical power take-off (PTO) Solar power tower, a type of solar power plant Tetration, a mathematical operation also known as power tower, hyperpower, or superexponentiation...
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transfer function, the solution is expressible compactly. The equation of tetration is a special case of Abel's equation, with f = exp. In the case of an...
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{\displaystyle \gamma } are irrational. It is not known if either of the tetrations n π {\displaystyle ^{n}\pi } or n e {\displaystyle ^{n}e} is rational...
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