## Tetration |

In **tetration** (or **hyper-4**) is

The first four

Addition *n*copies of 1 added to*a*.

Multiplication *n*copies of*a*combined by addition.

Exponentiation *n*copies of*a*combined by multiplication.

- Tetration
*n*copies of*a*combined by exponentiation, right-to-left.

Here, succession (*a′* = *a* + 1) is the most basic operation; addition (*a* + *n*) is a primary operation, though for natural numbers it can be thought of as a chained succession of n successors of a; multiplication ((*a* × *n*) is also a primary operation, though for natural numbers it can be thought of as a chained addition involving n numbers a. Exponentiation () can be thought of as a chained multiplication involving n numbers a, and analogously, tetration () can be thought of as a chained power involving n numbers a. Each of the operations above are defined by iterating the previous one; however, unlike the operations before it, tetration is not an

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 (which is integral in the first approach but may be generalized to fractional, real and complex *heights*, see below). Tetration is read as "the nth tetration of a".

Other Languages

čeština: Tetrace

dansk: Tetration

Deutsch: Potenzturm

español: Tetración

Esperanto: Supereksponento

français: Tétration

한국어: 테트레이션

italiano: Tetrazione

עברית: טטרציה

magyar: Tetráció

Nederlands: Tetratie

日本語: テトレーション

polski: Tetracja

português: Tetração

română: Tetrație

русский: Тетрация

Simple English: Tetration

српски / srpski: Тетрација

suomi: Tetraatio

svenska: Tetraering

Türkçe: Tetrasyon

українська: Тетрація

Tiếng Việt: Túc thừa

中文: 迭代冪次