quality:corruption, quality:correction
Introduction

The hyperoperations naturally extend the arithmetic operations of addition and multiplication as follows. Addition by a natural number is defined as iterated incrementation:

Multiplication by a natural number is defined as iterated addition:

For example,

Exponentiation for a natural power b {\displaystyle b} is defined as iterated multiplication, which Knuth denoted by a single up-arrow:

For example,

Tetration is defined as iterated exponentiation, which Knuth denoted by a “double arrow”:

For example,

Expressions are evaluated from right to left, as the operators are defined to be right-associative.

According to this definition,

This already leads to some fairly large numbers, but the hyperoperator sequence does not stop here.

Pentation, defined as iterated tetration, is represented by the “triple arrow”:

Hexation, defined as iterated pentation, is represented by the “quadruple arrow”:

and so on. The general rule is that an n {\displaystyle n} -arrow operator expands into a right-associative series of (n − 1 {\displaystyle n-1})-arrow operators. Symbolically,

Examples: