In
mathematics, the
hyperoperation sequence is an infinite
sequence of arithmetic operations (called
hyperoperations) that starts with the
unary operation of
successor (
n = 0), then continues with the
binary operations of
addition (
n = 1),
multiplication (
n = 2), and
exponentiation (
n = 3), after which the sequence proceeds with further binary operations extending beyond exponentiation, using
right-associativity. 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 (
n = 4),
pentation (
n = 5), hexation (
n = 6), etc.) and can be written as using
n - 2 arrows in
Knuth's up-arrow notation. Each hyperoperation may be understood
recursively in terms of the previous one by:
- (m = 0)
