associativity

property of binary operations allowing sequences of operations to be regrouped without changing their value
Thing mathematical_property Q177251
associativity
File:Associativity of binary operations.svg: Talonnn derivative work: Stephan Kulla (User:Stephan Kulla) · Public Domain · Wikimedia
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associativity

Summary

associativity is a mathematical property[1]. associativity draws 296 Wikipedia views per month (mathematical_property category, ranking #4 of 26).[2]

Key Facts

  • associativity's image is recorded as Associativity of binary operations (without question marks).svg[3].
  • associativity's instance of is recorded as mathematical property[4].
  • associativity's instance of is recorded as rule of replacement[5].
  • associativity's Freebase ID is recorded as /m/0gvsfvc[6].
  • associativity's Gran Enciclopèdia Catalana ID is recorded as 0081416[7].
  • associativity's described by source is recorded as Great Soviet Encyclopedia (1926–1947)[8].
  • associativity's described by source is recorded as Brockhaus and Efron Encyclopedic Dictionary[9].
  • associativity's described by source is recorded as Armenian Soviet Encyclopedia, vol. 3[10].
  • associativity's used by is recorded as addition[11].
  • associativity's used by is recorded as multiplication[12].
  • associativity's used by is recorded as union[13].
  • associativity's defining formula is recorded as \forall x,y\colon (x\star y)\star z=x\star (y\star z)[14].
  • associativity's MathWorld ID is recorded as Associative[15].
  • associativity's Great Russian Encyclopedia Online ID is recorded as 1835193[16].
  • associativity's nLab ID is recorded as associativity[17].
  • associativity's Elhuyar ZTH ID is recorded as 032872[18].
  • associativity's on focus list of Wikimedia project is recorded as Wikipedia:Vital articles/Level/4[19].
  • associativity's Dictionary of Algorithms and Data Structures ID is recorded as associative[20].
  • associativity's maintained by WikiProject is recorded as WikiProject Mathematics[21].
  • associativity's Microsoft Academic ID is recorded as 159423971[22].
  • associativity's Australian Educational Vocabulary ID is recorded as scot/12412[23].
  • associativity's Group Properties article ID is recorded as Associative_binary_operation[24].
  • associativity's OpenAlex ID is recorded as C159423971[25].
  • associativity's Gran Enciclopèdia Catalana ID is recorded as associativitat[26].
  • associativity's FOLDOC ID is recorded as associativity[27].

Body

Works and Contributions

Things named for associativity include associahedron[28], a polytope family[29].

Why It Matters

associativity draws 296 Wikipedia views per month (mathematical_property category, ranking #4 of 26).[2] associativity has Wikipedia articles in 30 language editions, a strong signal of global cultural recognition.[30] associativity is known by 61 alternative names across languages and contexts.[31]

Entities named for associativity include associahedron[28], a polytope family[29].

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . wikidata.org.
  14. [16] . wikidata.org.
  15. [17] . wikidata.org.
  16. [18] . wikidata.org.
  17. [19] . wikidata.org.
  18. [20] . wikidata.org.
  19. [21] . wikidata.org.
  20. [22] . wikidata.org.
  21. [23] . wikidata.org.
  22. [24] . wikidata.org.
  23. [25] . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.
  24. [26] . wikidata.org.
  25. [27] . wikidata.org.

Inverse relationships (entities pointing at this one)

  1. [28] . wikidata.org. → on this site

Inline context (facts about related entities)

  1. [29] . Wikidata. wikidata.org. → on this site

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [30] . Wikidata sitelinks. wikidata.org.
  3. [31] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). associativity. Retrieved May 3, 2026, from https://4ort.xyz/entity/associativity
MLA “associativity.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/associativity.
BibTeX @misc{4ortxyz_associativity_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{associativity}}, year = {2026}, url = {https://4ort.xyz/entity/associativity}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): associativity — https://4ort.xyz/entity/associativity (retrieved 2026-05-03)

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