# 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:

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

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### E

### M

## Pages in category "Examples of Well-Defined Mappings"

The following 11 pages are in this category, out of 11 total.