ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Function
▼ Real collection function
▼ Euclidean real function
▼ Real function
▼ Rational function
▼ Integer function
▼ Natural number function
Definition D1672
Collatz function
Formulation 0
The Collatz function is the D4949: 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: 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
▶ C3: Collatz conjecture