Bowers' operators
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Let , the hyperoperation. That is
Invented by Jonathan Bowers, the first operator is and it's 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 .
For every fixed positive integer , there is an operator with sets of brackets. The domain of is , and the codomain of the operator is .
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 .
Numbers like TREE(3) are unattainable with Bowers' operators, but Graham's number lies between and .[1]
References
- ↑ Lua error in package.lua at line 80: module 'strict' not found.