See formal sum in All languages combined, or Wiktionary
{ "forms": [ { "form": "formal sums", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "formal sum (plural formal sums)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Algebra", "orig": "en:Algebra", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "50 50", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" } ], "glosses": [ "An expression which looks like a sum but where the symbol + has a purely symbolic role, in the sense that the summands cannot be meaningfully combined.", "An element of a free abelian group or vector space regarded as a sum of basis elements." ], "id": "en-formal_sum-en-noun-~Rk7VoeV", "links": [ [ "mathematics", "mathematics" ], [ "expression", "expression" ], [ "sum", "sum" ], [ "+", "+" ], [ "symbolic", "symbolic" ], [ "algebra", "algebra" ], [ "free", "free" ], [ "abelian", "abelian" ], [ "group", "group" ], [ "vector space", "vector space" ], [ "basis", "basis" ], [ "element", "element" ] ], "raw_glosses": [ "(mathematics) An expression which looks like a sum but where the symbol + has a purely symbolic role, in the sense that the summands cannot be meaningfully combined.", "(algebra) An element of a free abelian group or vector space regarded as a sum of basis elements." ], "topics": [ "algebra", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "50 50", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "50 50", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" } ], "glosses": [ "An expression which looks like a sum but where the symbol + has a purely symbolic role, in the sense that the summands cannot be meaningfully combined.", "A sum of an infinite sequence of numbers considered as an indeterminate object, in the sense of being subject to certain algebraic manipulations but not necessarily convergent." ], "id": "en-formal_sum-en-noun-8ocjZTF2", "links": [ [ "mathematics", "mathematics" ], [ "expression", "expression" ], [ "sum", "sum" ], [ "+", "+" ], [ "symbolic", "symbolic" ], [ "series", "series" ], [ "sequence", "sequence" ], [ "indeterminate", "indeterminate" ], [ "algebraic", "algebraic" ], [ "convergent", "convergent" ] ], "raw_glosses": [ "(mathematics) An expression which looks like a sum but where the symbol + has a purely symbolic role, in the sense that the summands cannot be meaningfully combined.", "(of a series) A sum of an infinite sequence of numbers considered as an indeterminate object, in the sense of being subject to certain algebraic manipulations but not necessarily convergent." ], "raw_tags": [ "of a series" ], "topics": [ "mathematics", "sciences" ] } ], "word": "formal sum" }
{ "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English multiword terms", "English nouns", "Pages with 1 entry", "Pages with entries" ], "forms": [ { "form": "formal sums", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "formal sum (plural formal sums)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ "en:Algebra", "en:Mathematics" ], "glosses": [ "An expression which looks like a sum but where the symbol + has a purely symbolic role, in the sense that the summands cannot be meaningfully combined.", "An element of a free abelian group or vector space regarded as a sum of basis elements." ], "links": [ [ "mathematics", "mathematics" ], [ "expression", "expression" ], [ "sum", "sum" ], [ "+", "+" ], [ "symbolic", "symbolic" ], [ "algebra", "algebra" ], [ "free", "free" ], [ "abelian", "abelian" ], [ "group", "group" ], [ "vector space", "vector space" ], [ "basis", "basis" ], [ "element", "element" ] ], "raw_glosses": [ "(mathematics) An expression which looks like a sum but where the symbol + has a purely symbolic role, in the sense that the summands cannot be meaningfully combined.", "(algebra) An element of a free abelian group or vector space regarded as a sum of basis elements." ], "topics": [ "algebra", "mathematics", "sciences" ] }, { "categories": [ "en:Mathematics" ], "glosses": [ "An expression which looks like a sum but where the symbol + has a purely symbolic role, in the sense that the summands cannot be meaningfully combined.", "A sum of an infinite sequence of numbers considered as an indeterminate object, in the sense of being subject to certain algebraic manipulations but not necessarily convergent." ], "links": [ [ "mathematics", "mathematics" ], [ "expression", "expression" ], [ "sum", "sum" ], [ "+", "+" ], [ "symbolic", "symbolic" ], [ "series", "series" ], [ "sequence", "sequence" ], [ "indeterminate", "indeterminate" ], [ "algebraic", "algebraic" ], [ "convergent", "convergent" ] ], "raw_glosses": [ "(mathematics) An expression which looks like a sum but where the symbol + has a purely symbolic role, in the sense that the summands cannot be meaningfully combined.", "(of a series) A sum of an infinite sequence of numbers considered as an indeterminate object, in the sense of being subject to certain algebraic manipulations but not necessarily convergent." ], "raw_tags": [ "of a series" ], "topics": [ "mathematics", "sciences" ] } ], "word": "formal sum" }
Download raw JSONL data for formal sum meaning in English (2.4kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.