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Commutative property

Property of some mathematical operations

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General referenceInterpretive dossier study · Crown Archives visual atlas
Record originEnglish Wikipedia
Text licenseCC BY-SA 4.0
Source revisionSep 12, 2026
Entity authoritySource title only
Source-derived summary

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it ; such operations are not commutative, and so are referred to as noncommutative operations.

Editorial summary

Begin with the source’s own compact description: “Commutative property” is property of some mathematical operations. The dossier treats that line as a proposition to test through Commutative, property and Property, not as a finished interpretation.

Editorial reviewA concise reference frame for defining the subject, testing terminology and identifying the institution closest to the evidence. The current 101-word lead offers orientation but no explicit four-digit date, so chronology should not be assumed. The selected authority fields contribute no independent date. For this dossier, Commutative, property and Property is the immediate research focus.
Editorial analysis

Why this record matters

The phrase “property of some mathematical operations” supplies a clear boundary for inquiry. It also exposes the unanswered questions: who defined that boundary, when it became stable and which sources sit outside it.

Evidence profile

The citation trail is more important than the brevity of the summary: it shows where individual claims can be examined in context. The source revision retrieved here is dated Sep 12, 2026.

Critical limits

The absence of detail may reflect summary conventions rather than a lack of surviving documentation. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.

How to read it

Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.

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The closest primary source, responsible institution and strongest cited specialist reference.

Three-step research path

  1. Establish the record: confirm the title “Commutative property”, its source revision and the description used here.
  2. Expand the search: follow Commutative property primary sources, Commutative property archive and Commutative research across catalogues and specialist indexes.
  3. Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.

Questions for further research

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Source & attribution

This entry incorporates text from “Commutative property” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.