See lower limit on Wiktionary
{ "antonyms": [ { "word": "upper limit" } ], "forms": [ { "form": "lower limits", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "lower limit (plural lower limits)", "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": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Finnish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematical analysis", "orig": "en:Mathematical analysis", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "The lower limit of a sequence of real numbers is the real number which can be found as follows: remove the first term of the sequence in order to obtain the \"first subsequence.\" Then remove the first term of the first subsequence in order to obtain the \"second subsequence.\" Repeat the removal of first terms in order to obtain a \"third subsequence,\" \"fourth subsequence,\" etc. Find the infimum of each of these subsequences, then find the supremum of all of these infimums. This supremum is the lower limit." ], "id": "en-lower_limit-en-noun-8QWPFhVr", "links": [ [ "mathematical analysis", "mathematical analysis" ], [ "real numbers", "real numbers" ], [ "infimum", "infimum" ], [ "supremum", "supremum" ] ], "raw_glosses": [ "(mathematical analysis) The lower limit of a sequence of real numbers is the real number which can be found as follows: remove the first term of the sequence in order to obtain the \"first subsequence.\" Then remove the first term of the first subsequence in order to obtain the \"second subsequence.\" Repeat the removal of first terms in order to obtain a \"third subsequence,\" \"fourth subsequence,\" etc. Find the infimum of each of these subsequences, then find the supremum of all of these infimums. This supremum is the lower limit." ], "synonyms": [ { "word": "limit inferior" } ], "topics": [ "mathematical-analysis", "mathematics", "sciences" ], "translations": [ { "code": "fi", "lang": "Finnish", "sense": "the lower limit of a sequence of real numbers", "word": "alaraja-arvo" }, { "code": "fi", "lang": "Finnish", "sense": "the lower limit of a sequence of real numbers", "word": "alaraja" }, { "code": "pl", "lang": "Polish", "sense": "the lower limit of a sequence of real numbers", "tags": [ "feminine" ], "word": "dolna granica" } ] } ], "word": "lower limit" }
{ "antonyms": [ { "word": "upper limit" } ], "forms": [ { "form": "lower limits", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "lower limit (plural lower limits)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English multiword terms", "English nouns", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Terms with Finnish translations", "Terms with Polish translations", "en:Mathematical analysis" ], "glosses": [ "The lower limit of a sequence of real numbers is the real number which can be found as follows: remove the first term of the sequence in order to obtain the \"first subsequence.\" Then remove the first term of the first subsequence in order to obtain the \"second subsequence.\" Repeat the removal of first terms in order to obtain a \"third subsequence,\" \"fourth subsequence,\" etc. Find the infimum of each of these subsequences, then find the supremum of all of these infimums. This supremum is the lower limit." ], "links": [ [ "mathematical analysis", "mathematical analysis" ], [ "real numbers", "real numbers" ], [ "infimum", "infimum" ], [ "supremum", "supremum" ] ], "raw_glosses": [ "(mathematical analysis) The lower limit of a sequence of real numbers is the real number which can be found as follows: remove the first term of the sequence in order to obtain the \"first subsequence.\" Then remove the first term of the first subsequence in order to obtain the \"second subsequence.\" Repeat the removal of first terms in order to obtain a \"third subsequence,\" \"fourth subsequence,\" etc. Find the infimum of each of these subsequences, then find the supremum of all of these infimums. This supremum is the lower limit." ], "topics": [ "mathematical-analysis", "mathematics", "sciences" ] } ], "synonyms": [ { "word": "limit inferior" } ], "translations": [ { "code": "fi", "lang": "Finnish", "sense": "the lower limit of a sequence of real numbers", "word": "alaraja-arvo" }, { "code": "fi", "lang": "Finnish", "sense": "the lower limit of a sequence of real numbers", "word": "alaraja" }, { "code": "pl", "lang": "Polish", "sense": "the lower limit of a sequence of real numbers", "tags": [ "feminine" ], "word": "dolna granica" } ], "word": "lower limit" }
Download raw JSONL data for lower limit meaning in All languages combined (2.3kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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.