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

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

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...

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

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...

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

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 21 of them are: Also see Fermat number, tetration and lower hyperoperations. All of these numbers over 4 end with the digit...

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 ∞...

= 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...

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...

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

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

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

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...

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

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...

maps Logistic map Lorenz attractor Lorenz-96 Iterated function system Tetration Ackermann function Horseshoe map Hénon map Arnold's cat map Population...

{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)...

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

pandigital number 387,420,489 = 196832 = 7293 = 276 = 99 = 318 and in tetration notation 29 387,426,321 = Leyland number using 3 & 18 (318 + 183) 400...

terms, is correct to the first decimal place when n is positive. Also see Tetration: f n(1) = n√2. Using the other fixed point a = f(4) = 4 causes the series...

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

functions, but much more slowly than double exponential functions. However, tetration and the Ackermann function grow faster. See Big O notation for a comparison...

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

Lambert W function. Some examples of functions that are not elementary: tetration the gamma function non-elementary Liouvillian functions, including the...

sequence, together with the naming convention now used for these operations (tetration, pentation, hexation, etc.). Besides mathematical logic (in which he held...

function is a linear combination of its partial derivatives Euler's infinite tetration theorem – About the limit of iterated exponentiation Euler's rotation...

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