mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though Knuth's...

fifth hyperoperation. Pentation is defined to be repeated tetration, similarly to how tetration is repeated exponentiation, exponentiation is repeated multiplication...

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...

now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation, etc., for the extended operations beyond exponentiation. The...

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 ∞...

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...

exponentiation; this operation is sometimes called hyper-4 or tetration. Iterating tetration leads to another operation, and so on, a concept named hyperoperation...

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...

= 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...

multiple up arrows, such as ⇈, for iterated, or repeated, exponentiation (tetration). The quantum theory of electron spin uses either upward or downward arrows...

\uparrow 2\uparrow \uparrow (3+2\uparrow \uparrow 8),} which contains three tetrations. In 2019 this was further improved to: N ″ = ( 2 ↑↑ 5138 ) ⋅ ( ( 2 ↑↑...

by which the magnitude of a googolplex could be represented, such as tetration, hyperoperation, Knuth's up-arrow notation, Steinhaus–Moser notation,...

hyperoperations, used to build addition, multiplication, exponentiation, tetration, etc. It was studied in 1986 in an investigation involving generalization...

the set of real or rational numbers, is not commutative or associative. Tetration ( ↑↑ {\displaystyle \uparrow \uparrow } ), as a binary operation on the...

Mobile collaboration and cloud computing  United States — February 2014 Tetration Analytics Data Center Analytics and Security Solution  United States —...

{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)...

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,...

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...

Wiktionary, the free dictionary. ^^ may refer to: A kaomoji Tetration, the ASCII form of the tetration operator Record separator, control character in the caret...

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...

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...

H-function Hyper operators Iterated logarithm Pentation Super-logarithms Tetration Lambert W function: Inverse of f(w) = w exp(w). Lamé function Mathieu...

Hyperexponential can refer to: The hyperexponential distribution in probability. Tetration, also known as hyperexponentiation. This disambiguation page lists articles...

} This sum is transcendental because it is a Liouville number. Like tetration, there is currently no accepted method of extension of the exponential...

more classes of growth behavior, like the hyperoperations beginning at tetration, and A ( n , n ) {\displaystyle A(n,n)} , the diagonal of the Ackermann...

introduced by Hans Maurer (1901) and Reuben Louis Goodstein (1947) for tetration, or with David Patterson Ellerman's (1995) nx pre-superscript notation...

number is too large to reasonably express using exponentiation or even tetration. For more about modern usage for large numbers, see Large numbers. To...

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...

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...

{\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...