Knuth's up-arrow notation is a way of saying very big numbers.

In order to be able to write it down, we have to use Knuth's up-arrow notation.

Graham's number illustrates this as Knuth's up-arrow notation is used.

However, these expressions become arbitrarily large when dealing with systems such as Knuth's up-arrow notation.

They are often written using Knuth's up-arrow notation.

Pentation can be written in Knuth's up-arrow notation as or .

Similarly, (in Knuth's up-arrow notation) is considered only a formal expression which does not correspond to a natural number.

Continuing the pattern in Knuth's up-arrow notation, , and so on, for any number of up arrows.

This sequence of operations is expressed by the Ackermann function and Knuth's up-arrow notation.

The upward-pointing arrow is now used as a form of iterated exponentiation in Knuth's up-arrow notation.

A chain of length 3 corresponds to Knuth's up-arrow notation and hyper operators:

(The general term is given using Knuth's up-arrow notation; the operator is equivalent to tetration.)

In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976.

Even power towers of the form are useless for this purpose, although it can be easily described by recursive formulas using Knuth's up-arrow notation or the equivalent, as was done by Graham.

Some numbers are so large that multiple arrows of Knuth's up-arrow notation become too cumbersome; then an n-arrow operator is useful (and also for descriptions with a variable number of arrows), or equivalently, hyper operators.

In pure mathematics, the magnitude of a googolplex could be related to other forms of large-number notation such as tetration, Knuth's up-arrow notation, Steinhaus-Moser notation, or Conway chained arrow notation.