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Blueberry comments on Bizarre Illusions - Less Wrong
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Ackermann function
Knuth's arrow notation
Cool, thanks. It seems like one of my first tries was producing numbers similar to the Ackermann function. Knuth's arrow notation essentially takes over after multiplication. But those two articles will give me enough to read to keep moving on. :)
Do you know of any that go the other way into smaller and smaller numbers?
EDIT: I found the right subject name through links on your links. It is called hyperoperation.
1 / Ackermann function.
Sure, that works, but it isn't exactly what I am looking for. Is it possible to express the division operator in a manner similar to how multiplication can be expressed using addition? My instinct is telling me probably not.
You can have inverse operations for the higher operations as well. 4^4 is 256, so you can think of 4 as the "tetrated root" of 256. Also see this
(I'm using 'tetrating' as a term for the operation after exponentiation: in other words, 4 tetrated to the 4th is 4^(4^(4^4))).
Two problems: there may not be a clear way to define tetrating and higher operations to fractional amounts, and exponentiation and up aren't associative, so you need a convention for what to do with the parentheses.