preimage

See also: préimage

English

Etymology

From pre- +‎ image.

Pronunciation

• Rhymes: -ɪmɪdʒ

Noun

preimage (plural preimages)

1. (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 $f:\mathbb {R} \rightarrow \mathbb {R} :f(x)=x^{2}$ 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.

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

• preimage attack

Related terms

• image

Translations

set of all elements that map into a given subset of the codomain of a function

• Chinese:

  Mandarin: 原像 (zh) (yuánxiàng)

• Esperanto: prabildo, kontraŭbildo, malbildo
• Finnish: alkukuva
• French: préimage (fr) f, image réciproque (fr) f
• German: Urbild (de) n
• Polish: przeciwobraz (pl) m
• Portuguese: pré-imagem f
• Spanish: imagen inversa f, antiimagen f, contraimagen f

Further reading

• Image (mathematics) on Wikipedia.Wikipedia
• Kernel (linear algebra) on Wikipedia.Wikipedia