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preimage. In DICTIOUS you will not only get to know all the dictionary meanings for the word
preimage, but we will also tell you about its etymology, its characteristics and you will know how to say
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English
Etymology
From pre- + image.
Pronunciation
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 under the function is the set .
- 1967 , 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.
Synonyms
- (set of all elements that map into a given subset of the codomain of a function): inverse image
Hyponyms
- (set of all elements that map into a given subset of the codomain of a function): kernel
Derived terms
Translations
set of all elements that map into a given subset of the codomain of a function
Further reading