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
Bijective map
Set of bijections
Countable set
Definition D17
Finite set
Formulation 0
Let $\mathbb{N}$ be the D225: Set of natural numbers.
A D11: Set $X$ is a finite set if and only if \begin{equation} \exists \, N \in \mathbb{N} : \text{Bij}(\{ 1, \ldots, N \} \to X) \neq \emptyset \end{equation}
Children
Cofinite set
Results
Finite cartesian product of finite sets is finite