Commutativity

Part of speech: noun

Definitions

1. A mathematical attribute indicating that the outcomes remain unchanged regardless of the arrangement of elements involved in a binary operation
2. This property highlights that the result is invariant to the reordering of operands in a specific operation
3. The quality of a binary operation that ensures swapping the operands does not change the outcome

Etymology: "Commutativity" is built from "commutative" plus the suffix "-ity", which marks a quality or state. The adjective "commutative" comes from the Latin "commutativus", meaning changeable or interchangeable, from "commutare", to exchange or alter completely. The "com-" prefix adds the sense of "together" or "with each other," and "mutare" is "to change." The suffix has a longer path than the base word. It descends from Proto-Indo-European *-teh₂ts, which passed through Latin "-itas" (a suffix forming abstract nouns from adjectives), then Old French "-ite," and Middle English "-ite." English later settled on the form "-ity," so the suffix arrived in English as an inherited ending that had been reshaped many times on the way. Taken together, the word names the quality of being changeable in the sense that matters to mathematics: an operation is commutative when the order of its operands does not alter the result. The word's parts describe exactly that idea of exchange, with the Latin roots of "mutare" carrying the meaning of change into the precise sense of swapping.

Synonyms: commutative property