See Banach-Tarski paradox on Wiktionary
{ "etymology_text": "Named after Polish mathematicians Stefan Banach and Alfred Tarski.", "head_templates": [ { "args": {}, "expansion": "Banach-Tarski paradox", "name": "en-proper noun" } ], "lang": "English", "lang_code": "en", "pos": "name", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Group theory", "orig": "en:Group theory", "parents": [ "Algebra", "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" }, { "kind": "topical", "langcode": "en", "name": "Set theory", "orig": "en:Set theory", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "A theorem in set-theoretic geometry, which states that given a solid ball in three‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball." ], "id": "en-Banach-Tarski_paradox-en-name-6f9WtCGe", "links": [ [ "mathematics", "mathematics" ], [ "theorem", "theorem" ], [ "set-theoretic", "set-theoretic" ], [ "geometry", "geometry" ], [ "solid", "solid" ], [ "ball", "ball" ], [ "decomposition", "decomposition" ], [ "finite", "finite" ], [ "disjoint", "disjoint" ], [ "subset", "subset" ], [ "identical", "identical" ] ], "raw_glosses": [ "(mathematics) A theorem in set-theoretic geometry, which states that given a solid ball in three‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball." ], "topics": [ "mathematics", "sciences" ], "wikipedia": [ "Alfred Tarski", "Banach-Tarski paradox", "Stefan Banach" ] } ], "word": "Banach-Tarski paradox" }
{ "etymology_text": "Named after Polish mathematicians Stefan Banach and Alfred Tarski.", "head_templates": [ { "args": {}, "expansion": "Banach-Tarski paradox", "name": "en-proper noun" } ], "lang": "English", "lang_code": "en", "pos": "name", "senses": [ { "categories": [ "English entries with incorrect language header", "English eponyms", "English lemmas", "English multiword terms", "English proper nouns", "English uncountable nouns", "Pages with 1 entry", "Pages with entries", "en:Group theory", "en:Mathematics", "en:Set theory" ], "glosses": [ "A theorem in set-theoretic geometry, which states that given a solid ball in three‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball." ], "links": [ [ "mathematics", "mathematics" ], [ "theorem", "theorem" ], [ "set-theoretic", "set-theoretic" ], [ "geometry", "geometry" ], [ "solid", "solid" ], [ "ball", "ball" ], [ "decomposition", "decomposition" ], [ "finite", "finite" ], [ "disjoint", "disjoint" ], [ "subset", "subset" ], [ "identical", "identical" ] ], "raw_glosses": [ "(mathematics) A theorem in set-theoretic geometry, which states that given a solid ball in three‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball." ], "topics": [ "mathematics", "sciences" ], "wikipedia": [ "Alfred Tarski", "Banach-Tarski paradox", "Stefan Banach" ] } ], "word": "Banach-Tarski paradox" }
Download raw JSONL data for Banach-Tarski paradox meaning in All languages combined (1.6kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 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.