preimage

Noun

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Noun

**preimage** (*plural* preimages)

- (
*mathematics*) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (*formally*) given a function ƒ :*X*→*Y*and a subset*B*⊆*Y*, the set ƒ^{−1}(*B*) = {*x*∈*X*: ƒ(*x*) ∈*B*}.*The***preimage**of \{4, 9\} under the function f : \R\rightarrow \R:f(x)=x^2 is the set \{-3,-2,+2,+3\}.

**1967**[Academic Press], Francois Treves,*Topological Vector Spaces, Distributions and Kernels*, 2006, Dover, page 22 ↗,- The
**preimage**of a neighborhood*U*of 0 in*E*must be a neighborhood of (0,*x*), since (0,*x*) is mapped into 0.

- The
**2003**, Sergei K. Lando, Alexander K. Zvonkin,*Graphs on Surfaces and Their Applications*, Springer, page 56 ↗,- Previously, maps and hypermaps were constructed as the
**preimages**of a segment joining two of the three critical values.

- Previously, maps and hypermaps were constructed as the
**2005**, Oded Goldreich,*Foundations of Cryptography: A Primer*, now Publishers, page 24 ↗,- Loosely speaking, saying that a function
*f*is one-way implies that given*y*(in the range of*f*) it is infeasible to find a**preimage**of*y*under*f*.

- Loosely speaking, saying that a function

- (
*set of all elements that map into a given subset of the codomain of a function*) inverse image

- German: Urbild
- Portuguese: pré-imagem

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.003