See preimage in All languages combined, or Wiktionary
Download JSON data for preimage meaning in English (5.1kB)
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "pre",
"3": "image"
},
"expansion": "pre- + image",
"name": "prefix"
}
],
"etymology_text": "pre- + image.",
"forms": [
{
"form": "preimages",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "preimage (plural preimages)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English terms prefixed with pre-",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Mandarin terms with redundant transliterations",
"parents": [
"Terms with redundant transliterations",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"derived": [
{
"word": "preimage attack"
}
],
"examples": [
{
"text": "The preimage of #x5C;#x7B;4,9#x5C;#x7D; under the function f#x3A;#x5C;R#x5C;rightarrow#x5C;R#x3A;f(x)#x3D;x² is the set #x5C;#x7B;-3,-2,#x2B;2,#x2B;3#x5C;#x7D;.",
"type": "example"
},
{
"text": "1967 [Academic Press], Francois Treves, Topological Vector Spaces, Distributions and Kernels, 2006, Dover, page 22,\nThe preimage of a neighborhood U of 0 in E must be a neighborhood of (0,x), since (0,x) is mapped into 0."
},
{
"ref": "2003, Sergei K. Lando, Alexander K. Zvonkin, Graphs on Surfaces and Their Applications, Springer, page 56",
"text": "Previously, maps and hypermaps were constructed as the preimages of a segment joining two of the three critical values.",
"type": "quotation"
},
{
"ref": "2005, Oded Goldreich, Foundations of Cryptography: A Primer, now Publishers, page 24",
"text": "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.",
"type": "quotation"
}
],
"glosses": [
"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}."
],
"hyponyms": [
{
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "kernel"
}
],
"id": "en-preimage-en-noun-z38YkgRB",
"links": [
[
"mathematics",
"mathematics"
],
[
"function",
"function"
],
[
"domain",
"domain"
],
[
"codomain",
"codomain"
]
],
"raw_glosses": [
"(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}."
],
"related": [
{
"word": "image"
}
],
"synonyms": [
{
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "inverse image"
}
],
"topics": [
"mathematics",
"sciences"
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "yuánxiàng",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "原像"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "prabildo"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "kontraŭbildo"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "malbildo"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "alkukuva"
},
{
"code": "fr",
"lang": "French",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"feminine"
],
"word": "préimage"
},
{
"code": "fr",
"lang": "French",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"feminine"
],
"word": "image réciproque"
},
{
"code": "de",
"lang": "German",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"neuter"
],
"word": "Urbild"
},
{
"code": "pl",
"lang": "Polish",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"masculine"
],
"word": "przeciwobraz"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"feminine"
],
"word": "pré-imagem"
},
{
"code": "es",
"lang": "Spanish",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"feminine"
],
"word": "imagen inversa"
},
{
"code": "es",
"lang": "Spanish",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"feminine"
],
"word": "antiimagen"
},
{
"code": "es",
"lang": "Spanish",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"feminine"
],
"word": "contraimagen"
}
],
"wikipedia": [
"Preimage"
]
}
],
"sounds": [
{
"rhymes": "-ɪmɪdʒ"
}
],
"word": "preimage"
}
{
"derived": [
{
"word": "preimage attack"
}
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "pre",
"3": "image"
},
"expansion": "pre- + image",
"name": "prefix"
}
],
"etymology_text": "pre- + image.",
"forms": [
{
"form": "preimages",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "preimage (plural preimages)",
"name": "en-noun"
}
],
"hyponyms": [
{
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "kernel"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "image"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English nouns",
"English terms prefixed with pre-",
"English terms with quotations",
"English terms with usage examples",
"Mandarin terms with redundant transliterations",
"Rhymes:English/ɪmɪdʒ",
"Rhymes:English/ɪmɪdʒ/3 syllables",
"en:Mathematics"
],
"examples": [
{
"text": "The preimage of #x5C;#x7B;4,9#x5C;#x7D; under the function f#x3A;#x5C;R#x5C;rightarrow#x5C;R#x3A;f(x)#x3D;x² is the set #x5C;#x7B;-3,-2,#x2B;2,#x2B;3#x5C;#x7D;.",
"type": "example"
},
{
"text": "1967 [Academic Press], Francois Treves, Topological Vector Spaces, Distributions and Kernels, 2006, Dover, page 22,\nThe preimage of a neighborhood U of 0 in E must be a neighborhood of (0,x), since (0,x) is mapped into 0."
},
{
"ref": "2003, Sergei K. Lando, Alexander K. Zvonkin, Graphs on Surfaces and Their Applications, Springer, page 56",
"text": "Previously, maps and hypermaps were constructed as the preimages of a segment joining two of the three critical values.",
"type": "quotation"
},
{
"ref": "2005, Oded Goldreich, Foundations of Cryptography: A Primer, now Publishers, page 24",
"text": "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.",
"type": "quotation"
}
],
"glosses": [
"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}."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"function",
"function"
],
[
"domain",
"domain"
],
[
"codomain",
"codomain"
]
],
"raw_glosses": [
"(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}."
],
"topics": [
"mathematics",
"sciences"
],
"wikipedia": [
"Preimage"
]
}
],
"sounds": [
{
"rhymes": "-ɪmɪdʒ"
}
],
"synonyms": [
{
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "inverse image"
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "yuánxiàng",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "原像"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "prabildo"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "kontraŭbildo"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "malbildo"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"word": "alkukuva"
},
{
"code": "fr",
"lang": "French",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"feminine"
],
"word": "préimage"
},
{
"code": "fr",
"lang": "French",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"feminine"
],
"word": "image réciproque"
},
{
"code": "de",
"lang": "German",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"neuter"
],
"word": "Urbild"
},
{
"code": "pl",
"lang": "Polish",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"masculine"
],
"word": "przeciwobraz"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"feminine"
],
"word": "pré-imagem"
},
{
"code": "es",
"lang": "Spanish",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"feminine"
],
"word": "imagen inversa"
},
{
"code": "es",
"lang": "Spanish",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"feminine"
],
"word": "antiimagen"
},
{
"code": "es",
"lang": "Spanish",
"sense": "set of all elements that map into a given subset of the codomain of a function",
"tags": [
"feminine"
],
"word": "contraimagen"
}
],
"word": "preimage"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-01 from the enwiktionary dump dated 2024-04-21 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.