Harman Patil (Editor)

Projection (set theory)

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

  • A set-theoretic operation typified by the jth projection map, written p r o j j , that takes an element x = ( x 1 ,   ,   x j ,   ,   x k ) of the Cartesian product ( X 1 × × X j × × X k ) to the value p r o j j ( x ) = x j .
  • A function that sends an element x to its equivalence class under a specified equivalence relation E, or, equivalently, a surjection from a set to another set. The function from elements to equivalence classes is a surjection, and every surjection corresponds to an equivalence relation under which two elements are equivalent when they have the same image. 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.
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    Projection (set theory) Wikipedia


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