• A set-theoretic operation typified by the j^th projection map, written $mathrm\{proj\}\_\{j\}!$, that takes an element $vec\{x\}\; =\; (x\_1,\; ldots,\; x\_j,\; ldots,\; x\_k)$ of the cartesian product $(X\_1\; times\; cdots\; times\; X\_j\; times\; cdots\; times\; X\_k)$ to the value $mathrm\{proj\}\_\{j\}(vec\{x\})\; =\; x\_j$.
• A function that sends an element x to its equivalence class under a specified equivalence relation E. The result of the mapping is written as [x] when E is understood, or written as [x]_E when it is necessary to make E explicit.

See also

• Cartesian product
• Projection (relational algebra)
• Relation