The

**constancy relation**on $X$ with respect to $f$ is the D4: Binary relation \begin{equation} \{ (x, y) \in X \times X : f(x) = f(y) \} \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Binary endorelation

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Binary endorelation

Formulation 0

Let $f : X \to Y$ be a D18: Map.

The**constancy relation** on $X$ with respect to $f$ is the D4: Binary relation
\begin{equation}
\{ (x, y) \in X \times X : f(x) = f(y) \}
\end{equation}

The