The

**set of euclidean natural numbers**with respect to $N \in \{ 1, 2, 3, \ldots \}$ is the D11: Set \begin{equation} \mathbb{N}^N = \prod_{n = 1}^N \mathbb{N} \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Collection of sets

▾ Set union

▾ Successor set

▾ Inductive set

▾ Set of inductive sets

▾ Set of natural numbers

▾ Set of integers

▾ Set of rational numbers

▾ Set of euclidean rational numbers

▾ Set of euclidean integers

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Collection of sets

▾ Set union

▾ Successor set

▾ Inductive set

▾ Set of inductive sets

▾ Set of natural numbers

▾ Set of integers

▾ Set of rational numbers

▾ Set of euclidean rational numbers

▾ Set of euclidean integers

Formulation 0

Let $\mathbb{N}$ be the D225: Set of natural numbers.

The**set of euclidean natural numbers** with respect to $N \in \{ 1, 2, 3, \ldots \}$ is the D11: Set
\begin{equation}
\mathbb{N}^N
= \prod_{n = 1}^N \mathbb{N}
\end{equation}

The

Child definitions