Projection (set theory)

From Wikinfo

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 <math>proj_{j}\!</math>, that takes an element <math>\vec{x} = (x_1,\ \ldots,\ x_j,\ \ldots,\ x_k)</math> of the cartesian product <math>(X_1 \times \cdots \times X_j \times \cdots \times X_k)</math> to the value <math>proj_{j}(\vec{x}) = x_j</math>.

• 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
• Relation
• Tacit extension

References

• Adapted from the Wikipedia article, "Projection_(set_theory)" http://en.wikipedia.org/wiki/Projection_(set_theory), used under the GNU Free Documentation License