Projection (set theory)

Projection (set theory)

In set theory, a projection is one of two closely related types of functions or operations, namely:

* 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 imes cdots imes X_j imes cdots imes 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.

ee also

* Cartesian product
* Projection (relational algebra)
* Relation


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