## Tetration |

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

Shown here are 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.

The above example is read as "the *nth* tetration of *a*". Each operation is defined by iterating the previous one. Tetration is not an

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 (an) 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 (which is integral in the first approach but may be generalized to fractional, real and complex *heights*, see below).

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