Concept information
Terme préférentiel
hyperoperation
Définition
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In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations in this context) that starts with a unary operation (the successor function with n = 0). The sequence continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3). After that, the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity. For the operations beyond exponentiation, the nth member of this sequence is named by 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 as using n − 2 arrows in Knuth's up-arrow notation. Each hyperoperation may be understood recursively in terms of the previous one by:
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Hyperoperation)
)\\cdots )))} _{\\displaystyle b{\\mbox{ copies of }}a},\\quad n\\geq 2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2b5b37b38e6798ec67d72e429a051aa7641fb571)
![{\\displaystyle ab=a[n-1]\\left(a\\left(b-1\
ight)\
ight),\\quad n\\geq 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/acfe8d681527fde64d3bcacced77270f96900f25)
Concept générique
Synonyme(s)
- hyperoperation sequence
Traductions
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français
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suite d'hyperopérateurs
URI
http://data.loterre.fr/ark:/67375/PSR-DZBL40KV-9
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