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:
“Yet time and space are but inverse measures of the force of the soul. The spirit sports with time.”
—Ralph Waldo Emerson (1803–1882)
“It is indeed typical that you Earth people refuse to believe in the superiority of any world but your own. Children looking into a magnifying glass, imagining the image you see is the image of your true size.”
—Franklin Coen. Joseph Newman. The Monitor (Douglas Spencer)