Inverse Image
"Preimage" redirects here. For the cryptographic attack on hash functions, see preimage attack.Let f be a function from X to Y. The preimage or inverse image of a set B ⊆ Y under f is the subset of X defined by
The inverse image of a singleton, denoted by f −1 or by f −1, is also called the fiber over y or the level set of y. The set of all the fibers over the elements of Y is a family of sets indexed by Y.
Again, if there is no risk of confusion, we may denote f −1 by f −1(B), and think of f −1 as a function from the power set of Y to the power set of X. The notation f −1 should not be confused with that for inverse function. The two coincide only if f is a bijection.
Read more about this topic: Image (mathematics)
Famous quotes containing the words inverse and/or image:
“The quality of moral behaviour varies in inverse ratio to the number of human beings involved.”
—Aldous Huxley (1894–1963)
“... But all the feelings that evoke in us the joy or the misfortune of a real person are only produced in us through the intermediary of an image of that joy or that misfortune; the ingeniousness of the first novelist was in understanding that, in the apparatus of our emotions, since the image is the only essential element, the simplification which consists of purely and simply suppressing the factual characters is a definitive improvement.”
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