High Quality Content by WIKIPEDIA articles! In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations) that starts with the unary operation of successor, then continues with the binary operations of addition, multiplication and exponentiation, after which the sequence proceeds with further binary operations extending beyond exponentiation. For the operations beyond exponentiation, the nth member of this sequence is named by Reuben Goodstein after the Greek prefix of n suffixed with -ation (such as tetration, pentation) and can be written using n-2 arrows in Knuth`s up-arrow notation (if the latter is properly extended to negative arrow-indices for the first three hyperoperations). Each hyperoperation is defined recursively in terms of the previous one, according to the recursion rule part of the definition, as in Knuth`s up-arrow version of the Ackermann function: