Pattern formation: Difference between revisions

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{{Unreferenced|date=December 2009}}
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In [[set theory]], a '''projection''' is one of two closely related types of [[function (mathematics)|function]]s or operations, namely:
 
* A [[set theory|set-theoretic]] operation typified by the ''j''<sup>th</sup> projection map, written <math>\mathrm{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>\mathrm{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'']<sub>''E''</sub> when it is necessary to make ''E'' explicit.
 
==See also==
* [[Cartesian product]]
* [[Projection (relational algebra)]]
* [[Projection (mathematics)]]
* [[Relation (mathematics)|Relation]]
 
{{DEFAULTSORT:Projection (Set Theory)}}
[[Category:Basic concepts in set theory]]
{{settheory-stub}}

Latest revision as of 15:32, 23 September 2014

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