(i) | $\text{Iso}(X \to Y)$ is the D2221: Set of bijections from $X$ to $Y$ |

**isomorphic**if and only if \begin{equation} \text{Iso}(X \to Y) \neq \emptyset \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Bijective map

▾ Set of bijections

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Bijective map

▾ Set of bijections

Formulation 0

Let $X$ and $Y$ each be a D11: Set such that

Then $X$ and $Y$ are **isomorphic** if and only if
\begin{equation}
\text{Iso}(X \to Y) \neq \emptyset
\end{equation}

(i) | $\text{Iso}(X \to Y)$ is the D2221: Set of bijections from $X$ to $Y$ |

Also known as

Equipollent sets, Equipotent sets, Equivalent sets, Equinumerous sets, Bijective sets