Category:Examples of Well-Defined Mappings

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This category contains examples of Well-Defined Mapping.

Let $f: S \to T$ be a mapping.

Let $\RR$ be an equivalence relation on $S$.

Let $S / \RR$ be the quotient set determined by $\RR$.

Let $\phi: S / \RR \to T$ be a mapping such that:

$\map \phi {\eqclass x \RR} = \map f x$

Then $\phi: S / \RR \to T$ is well-defined if and only if:

$\forall \tuple {x, y} \in \RR: \map f x = \map f y$