Hyperoperation facts for kids

Kids Encyclopedia Facts

A hyperoperation is a generalization of addition, multiplication, exponentiation, tetration, etc. They are often written using Knuth's up-arrow notation. Natural number level hyperoperations can be defined recursively as a piecewise function:

H_n(a, b) = \begin{cases} b + 1 & \text{if } n = 0 \\ a & \text{if } n = 1, b = 0 \\ 0 & \text{if } n = 2, b = 0 \\ 1 & \text{if } n \ge 3, b = 0 \\ H_{n-1}(a, H_n(a, b - 1)) & \text{otherwise} \end{cases}\,\!

See also

In Spanish: Hiperoperación para niños

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Hyperoperation Facts for Kids. Kiddle Encyclopedia.