# Category:Quotient Sets

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This category contains results about Quotient Sets.

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

For any $x \in S$, let $\eqclass x \RR$ be the $\RR$-equivalence class of $x$.

The **quotient set of $S$ induced by $\RR$** is the set $S / \RR$ of $\RR$-classes of $\RR$:

- $S / \RR := \set {\eqclass x \RR: x \in S}$

## Subcategories

This category has the following 10 subcategories, out of 10 total.

### C

### F

### Q

### R

## Pages in category "Quotient Sets"

The following 18 pages are in this category, out of 18 total.

### Q

### R

- Relation Induced by Partition is Equivalence
- Relation Induced by Quotient Set is Equivalence
- Relation Partitions Set iff Equivalence
- Relation Partitions Set iff Equivalence/Proof
- Renaming Mapping is Bijection
- Renaming Mapping is Well-Defined
- Renaming Mapping/Examples
- Renaming Mapping/Examples/Projection of Plane onto x-axis