What does commutatively mean?
The term commutatively refers to the property of a mathematical operation or function that remains unchanged under a swap of the operands. This means that the order of the operands does not affect the result of the operation. In other words, if a function f(x, y) is commutatively associative, then f(x, y) = f(y, x). This concept is crucial in various areas of mathematics, including algebra, geometry, and analysis. Commutativity is often used to describe the behavior of binary operations, such as addition, multiplication, and function composition. It is an essential property that helps to simplify mathematical expressions and proofs. In summary, commutatively is a term used to describe the commutative property of a mathematical operation or function, which remains unchanged under a swap of the operands.
adverbUsed to indicate that a mathematical operation or function is commutative, meaning that the order of the operands does not change the result.
- Used to indicate that a mathematical operation or function is commutative.
"The function f(x, y) = x + y is commutatively associative, as f(x, y) = f(y, x)."
"The function f(x, y) = x + y is commutatively associative, as f(x, y) = f(y, x)."
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of commutatively
The word commutatively originates from the Latin word 'mutare,' meaning 'to change' or 'to alter.' The term commutative was first used in mathematics in the 17th century to describe the property of a binary operation that remains unchanged under a swap of the operands. Over time, the term commutatively emerged as a variant of commutative, used to describe the same property in a more specific context.
How commutatively is actually used
In mathematics, commutativity is often used to describe the property of a binary operation or function that remains unchanged under a swap of the operands.