ThmDex – An index of mathematical definitions, results, and conjectures.
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
Definition D367
Set of integers
Formulation 1
Let $\mathbb{N}$ be the D225: Set of natural numbers such that
(i) $+ : \mathbb{N} \times \mathbb{N} \to \mathbb{N}$ is the D637: Natural number addition operation
(ii) \begin{equation} {\sim} : = \left\{ ((a, b), (c, d)) \in \mathbb{N}^2 \times \mathbb{N}^2 : a + d = b + c \right\} \end{equation}
The set of integers is the D180: Quotient set \begin{equation} \mathbb{Z} : = \mathbb{N}^2 / {\sim} \end{equation}
Children
D995: Integer
D4201: Set of rademacher integers
D368: Set of rational numbers