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 function that sends an element x to its equivalence class under a specified equivalence relation E,[2] or, equivalently, a surjection from a set to another set.[3] 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.

See also


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