▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map
▾ Bijective map
▾ Set of bijections
Isomorphic sets
Formulation 0
Let $X$ and $Y$ each be a D11: Set such that
(i) $\text{Iso}(X \to Y)$ is the D2221: Set of bijections from $X$ to $Y$
Then $X$ and $Y$ are isomorphic if and only if \begin{equation} \text{Iso}(X \to Y) \neq \emptyset \end{equation}
Also known as
Equipollent sets, Equipotent sets, Equivalent sets, Equinumerous sets, Bijective sets