Let , the hyperoperation. That is
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.CS1 maint: location (link)<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>