Definitions for tetration
tetra·tion

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1. tetrationnoun

   The arithmetic operator consisting of repeated exponentiation, by analogy with exponentiation being repeated multiplication and multiplication being repeated addition, a denoting a to the power of a to the power of ... to the power of a, in which a appears b times. Notation: a, or

2. Etymology: ; coined by Reuben Goodstein

WikipediaRate this definition:0.0 / 0 votes

1. Tetration

   In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though ↑↑ {\displaystyle \uparrow \uparrow } and the left-exponent xb are common. Under the definition as repeated exponentiation, n a {\displaystyle {^{n}a}} means a a ⋅ ⋅ a {\displaystyle {a^{a^{\cdot ^{\cdot ^{a}}}}}} , where n copies of a are iterated via exponentiation, right-to-left, i.e. the application of exponentiation n − 1 {\displaystyle n-1} times. n is called the "height" of the function, while a is called the "base," analogous to exponentiation. It would be read as "the nth tetration of a". It is the next hyperoperation after exponentiation, but before pentation. The word was coined by Reuben Louis Goodstein from tetra- (four) and iteration. Tetration is also defined recursively as a ↑↑ n := { 1 if n = 0 , a a ↑↑ ( n − 1 ) if n > 0 , {\displaystyle {a\uparrow \uparrow n}:={\begin{cases}1&{\text{if }}n=0,\\a^{a\uparrow \uparrow (n-1)}&{\text{if }}n>0,\end{cases}}} allowing for attempts to extend tetration to non-natural numbers such as real and complex numbers. The two inverses of tetration are called super-root and super-logarithm, analogous to the nth root and the logarithmic functions. None of the three functions are elementary. Tetration is used for the notation of very large numbers.

WikidataRate this definition:0.0 / 0 votes

1. Tetration

   In mathematics, tetration is the next hyper operator after exponentiation, and is defined as iterated exponentiation. The word was coined by Reuben Louis Goodstein, from tetra- and iteration. Tetration is used for the notation of very large numbers. Shown here are examples of the first four hyper operators, with tetration as the fourth: ⁕Additiona succeeded n times. ⁕Multiplicationa added to itself, n times. ⁕Exponentiationa multiplied by itself, n times. ⁕Tetrationa exponentiated by itself, n times. where each operation is defined by iterating the previous one. The peculiarity of the tetration among these operations is that the first three are generalized for complex values of n, while for tetration, no such regular generalization is yet established; and tetration is not considered an elementary function. Addition is the most basic operation, multiplication is also a primary operation, though for natural numbers it can be thought of as a chained addition involving n numbers a, and exponentiation can be thought of as a chained multiplication involving n numbers a. Analogously, tetration can be thought of as a chained power involving n numbers a. The parameter a may be called the base-parameter in the following, while the parameter n in the following may be called the height-parameter.

How to pronounce tetration?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say tetration in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of tetration in Chaldean Numerology is: 6

2. Pythagorean Numerology

   The numerical value of tetration in Pythagorean Numerology is: 5

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Tetration
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Tetration
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=tetration