Let , the hyperoperation. That is
Invented by Jonathan Bowers, the first operator is and it is defined:
The number inside the brackets can change. If it's two
Thus, we have
Operators beyond can also be made, the rule of it is the same as hyperoperation:
The next level of operators is , it to behaves like is to .
Another function means , where is the number of sets of brackets. It satisfies that for all integers , , , and . The domain of is , and the codomain of the operator is .
- Elwes, Richard (2010). Mathematics 1001: Absolutely Everything That Matters in Mathematics in 1001 Bite-Sized Explanations. Buffalo, New York 14205, United States: Firefly Books Inc. pp. 41–42. ISBN 978-1-55407-719-9.