Knuth's up-arrow notation is a useful way created by Donald Knuth to represent very large integers with iterated exponentiation.
The notation is defined by
- (m number of ns)
- with m number of ns on the RHS.
- with m number of ns on the RHS.
It is similar to standard exponentiation in a sense; for example:
The up-arrow notation gets cumbersome when many arrows are needed (eg Graham's number). The hyper operators and Conway chained arrow offer clearer alternatives: hyper(n,p+2,m) = n→m→p = n^…^m with p arrows. It is generally suggested that Knuth's arrow should be used for relatively smaller magnitude numbers, and the chained arrow or hyper operators for larger ones.