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)
“The paranoiac is the exact image of the ruler. The only difference is their position in the world.... One might even think the paranoiac the more impressive of the two because he is sufficient unto himself and cannot be shaken by failure.”
—Elias Canetti (b. 1905)