0. Set of symbols
1. Alphabet
2. Deduction system
3. Theory
4. Zermelo-Fraenkel set theory
5. Set
6. Binary cartesian set product
7. Binary relation
8. Map
9. Function
10. Real function
11. Euclidean real function
12. Basic real function
13. Basic rational function
14. Basic integer function
15. Basic natural number function
Collatz function
Formulation 0
The Collatz function is the D4949: Basic natural number function \begin{equation} \mathbb{N} + 1 \to \mathbb{N} + 1, \quad n \mapsto \begin{cases} 3 n + 1, \quad & n \in 2 \mathbb{N} + 1 \\ n / 2, \quad & n \in 2 \mathbb{N} \end{cases} \end{equation}
Formulation 1
The Collatz function is the D4949: Basic natural number function \begin{equation} \{ 1, 2, 3, \ldots \} \to \{ 1, 2, 3, \ldots \}, \quad n \mapsto \begin{cases} 3 n + 1, \quad & n \in \{ 1, 3, 5, \ldots \} \\ n / 2, \quad & n \in \{ 0, 2, 4, \ldots \} \end{cases} \end{equation}
Conjectures
» Collatz conjecture