Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
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Function
Real collection function
Euclidean real function
Real function
Rational function
Integer function
Natural number function
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
» Collatz conjecture