Projection (set theory)

• A set-theoretic operation typified by the j^th projection map, written, that takes an element of the Cartesian product to the value.
• A function that sends an element x to its equivalence class under a specified equivalence relation E, or, equivalently, a surjection from a set to another set. The function from elements to equivalence classes is a surjection, and every surjection corresponds to an equivalence relation under which two elements are equivalent when they have the same image. The result of the mapping is written as when E is understood, or written as _E when it is necessary to make E explicit.