Definition:Gödel's Beta Function
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Definition
Gödel's $\beta$ function $\beta: \N^3 \to \N$ is defined as:
- $\map \beta {x, y, z} = \map {\operatorname{rem} } {x, 1 + \paren {z + 1} \times y}$
where $\operatorname{rem}: \N^2 \to \N$ is defined as:
- $\map \rem {n, m} = \begin{cases}
\text{the remainder when } n \text{ is divided by } m & : m \ne 0 \\ 0 & : m = 0 \end{cases}$
Also see
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