# Projection (set theory)

(Redirected from Projection function)
• A set-theoretic operation typified by the jth projection map, written ${\displaystyle \mathrm {proj} _{j}\!}$, that takes an element ${\displaystyle {\vec {x}}=(x_{1},\ \ldots ,\ x_{j},\ \ldots ,\ x_{k})}$ of the Cartesian product ${\displaystyle (X_{1}\times \cdots \times X_{j}\times \cdots \times X_{k})}$ to the value ${\displaystyle \mathrm {proj} _{j}({\vec {x}})=x_{j}}$.[1]