---- > [!definition] Definition. ([[quotient set]]) > Let $X$ be a set and $\sim$ an [[equivalence relation]] on $X$. The **quotient** of $X$ by $\sim$, denoted $X \backslash {\sim}$, is the set of all [[equivalence class|equivalence classes]] of $\sim$. > \ > The **canonical projection** is the map $x \xmapsto{\pi} [x]$. ![[universal property of quotient sets#^theorem]] ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```