preimage
Jump to navigation
Jump to search
See also: préimage
English
[edit]Etymology
[edit]Pronunciation
[edit]- Rhymes: -ɪmɪdʒ
Noun
[edit]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 [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.
Synonyms
[edit]- (set of all elements that map into a given subset of the codomain of a function): inverse image
Hyponyms
[edit]- (set of all elements that map into a given subset of the codomain of a function): kernel
Derived terms
[edit]Related terms
[edit]Translations
[edit]set of all elements that map into a given subset of the codomain of a function
|
Further reading
[edit]Image (mathematics) on Wikipedia.Wikipedia
Kernel (linear algebra) on Wikipedia.Wikipedia