A D994: Rational number $q \in \mathbb{Q}$ is a

**P-adic basic rational number**with respect to $p$ if and only if \begin{equation} \exists \, n \in \mathbb{Z}, \, m \in \mathbb{N} : q = \frac{n}{p^m} \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

▾ Rational number

▾ 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

▾ Rational number

Formulation 0

Let $p$ be a D571: Prime integer.

A D994: Rational number $q \in \mathbb{Q}$ is a**P-adic basic rational number** with respect to $p$ if and only if
\begin{equation}
\exists \, n \in \mathbb{Z}, \, m \in \mathbb{N} :
q = \frac{n}{p^m}
\end{equation}

A D994: Rational number $q \in \mathbb{Q}$ is a

Child definitions