🔗 Tetration
In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. It is the next hyperoperation after exponentiation, but before pentation. The word was coined by Reuben Louis Goodstein from tetra- (four) and iteration.
Under the definition as repeated exponentiation, the notation means , where n copies of a are iterated via exponentiation, right-to-left, I.e. the application of exponentiation 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".
Tetration is also defined recursively as
- ,
allowing for attempts to extend tetration to non-natural numbers such as real and complex numbers.
The two inverses of tetration are called the super-root and the 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.
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- "Tetration" | 2010-05-02 | 28 Upvotes 11 Comments