A Notation invented by Knuth (1976) to represent Large Numbers in which evaluation proceeds from the right (Conway and Guy 1996, p. 60).

For example,

(1) | |||

(2) | |||

(3) | |||

(4) | |||

(5) |

is sometimes called a Power Tower. The values are called Ackermann Numbers.

**References**

Conway, J. H. and Guy, R. K. *The Book of Numbers.* New York: Springer-Verlag, pp. 59-62, 1996.

Guy, R. K. and Selfridge, J. L. ``The Nesting and Roosting Habits of the Laddered Parenthesis.'' *Amer. Math. Monthly*
**80**, 868-876, 1973.

Knuth, D. E. ``Mathematics and Computer Science: Coping with Finiteness. Advances in Our Ability to Compute are
Bringing Us Substantially Closer to Ultimate Limitations.'' *Science* **194**, 1235-1242, 1976.

Vardi, I. *Computational Recreations in Mathematica.* Redwood City, CA: Addison-Wesley, pp. 11
and 226-229, 1991.

© 1996-9

1999-05-25