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.
- 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.
- 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.
- (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