Projection (set theory)


{{Unreferenced|date=December 2009}}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(rojj
  , that takes an element
  →x = (x1 lderiv(⋅)s xj lderiv(⋅)s xk)
  of the cartesian product
  (X1 ⋅ cderiv(⋅)s ⋅ Xj ⋅ cderiv(⋅)s ⋅ Xk)
  to the value
  mathrm(rojj(→x) = xj
  .

• 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)
• Projection (mathematics)
• Relation

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