Everything about Hyperoperation
Generalization of addition, multiplication, exponentiation, tetration, etc.
In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations that starts with a unary operation. The sequence continues with the binary operations of addition, multiplication, and exponentiation. After that, the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity. For the operations beyond exponentiation, the n-th member of this sequence is named by Reuben Goodstein after the Greek prefix of n suffixed with -ation and can be written using n − 2 arrows in Knuth's up-arrow notation. Each hyperoperation may be understood recursively in terms of the previous one by: Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: HyperoperationA 5-minute orientation
- Pick up a classic book: HypernullarionThe most-reprinted book on the subject
- Read the landmark paper: Some remarks on congruences obtained from the L-fuzzy Nakano hyperoperationCited 6 times
- Go sideways: TetrationA closely related topic
- Go sideways: Ackermann functionA closely related topic
📖 Definitions
Noun One of a sequence of operations for compounding numbers that increase in growth iteratively.
🏆 Landmark papers (most cited)
📚 Books worth reading
HypernullarionIvan Futurologic Petrov · 2024
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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