Hyper-operators

The term "hyperoperation sequence" in mathematics refers to an endless chain of arithmetic operations, or "hyperoperations," that begin with an unary operation, or "successor function," with n = 0. The binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3) are then performed in the following order.

The series then continues with more binary operations employing right-associativity that go beyond exponentiation. Reuben Goodstein gave the name of the nth item of this series to the operations after exponentiation. These operations include tetration (n = 4), pentation (n = 5), hexation (n = 6), and others. The nth member of this sequence may be expressed using n-2 arrows in Knuth's up-arrow notation. Recursively understanding each hyperoperation in terms of the prior one may be done.