Knuth's up-arrow notation
In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. It is closely related to the Ackermann function and especially to the hyperoperation sequence. The idea is based on the fact that multiplication can be viewed as iterated addition and exponentiation as iterated multiplication. Continuing in this manner leads to tetration (iterated exponentiation) and to the remainder of the hyperoperation sequence, which is commonly denoted using Knuth arrow notation.
The ordinary arithmetical operations of addition, multiplication, and exponentiation are naturally extended into a sequence of hyperoperations as follows.
Multiplication by a natural number is defined as iterated addition:
For example,
Exponentiation for a natural power is defined as iterated multiplication, which Knuth denoted by a single up-arrow:
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