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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}.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences
Examples
- The preimage of #92;#123;4,9#92;#125; under the function f#58;#92;R#92;rightarrow#92;R#58;f(x)#61;x2 is the set #92;#123;-3,-2,#43;2,#43;3#92;#125;.
- 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Etymology tree Proto-Indo-European *per- Proto-Indo-European *preh2- Proto-Indo-European *-i Proto-Indo-European *préh2i? Proto-Italic *prai Proto-Italic *prai- Latin prae-lbor. Middle English pre- English pre- English image English preimage From pre- + image.
Across languages
Translations
13 source translations are retained for this English entry.
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Chinese Mandarin:
原像
(yuánxiàng)
— set of all elements that map into a given subset of the codomain of a function
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Esperanto:
prabildo
— set of all elements that map into a given subset of the codomain of a function
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Esperanto:
kontraŭbildo
— set of all elements that map into a given subset of the codomain of a function
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Esperanto:
malbildo
— set of all elements that map into a given subset of the codomain of a function
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Finnish:
alkukuva
— set of all elements that map into a given subset of the codomain of a function
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French:
préimage
— set of all elements that map into a given subset of the codomain of a function
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French:
image réciproque
— set of all elements that map into a given subset of the codomain of a function
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German:
Urbild
— set of all elements that map into a given subset of the codomain of a function
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Polish:
przeciwobraz
— set of all elements that map into a given subset of the codomain of a function
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Portuguese:
pré-imagem
— set of all elements that map into a given subset of the codomain of a function
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Spanish:
imagen inversa
— set of all elements that map into a given subset of the codomain of a function
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Spanish:
antiimagen
— set of all elements that map into a given subset of the codomain of a function
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Spanish:
contraimagen
— set of all elements that map into a given subset of the codomain of a function
