## Knuth's up-arrow notationThe Knuth's up-arrow notation is a notation for large numbers developed by the American mathematician Donald Knuth (1938–) in 1976. A single up-arrow () is the same as exponentiation: Two up-arrows together represent a power tower: m n = m ^{m^m^...^m} (a tower of height n), which is the same as the operation known
as hyper4 or tetration. This can very rapidly generate huge numbers. For
example:
2 2 = 2 2 = 4Three up-arrows together represent a still more vastly powerful operator, equivalent to hyper5 or pentation, or a power tower of power towers: For example: 2 2 = 2 2 = 4Similarly, so that, for example: 2 2 = 2 2 = 4Even up-arrow notation becomes cumbersome, however, when faced with staggeringly large numbers such as Graham's number. For such cases, more extensible systems such as Conway's chained arrow notation or Steinhaus-Moser notation are better suited. See also the Ackermann
function, to which up-arrow notation is closely related. ## Related category• SYMBOLS AND NOTATION | |||||

Home • About • Copyright © The Worlds of David Darling • Encyclopedia of Alternative Energy • Contact |