Commutativity Property

A Commutativity Property is a Binary Operation Property where the Operation Result is unchanged for any Permutation its Operands.

• AKA: Commutative, Commutativity, Commutative Law, Commutative Property.
• Context:
  • …
• Example(s):
  • a Symmetric Relation.
  • a Symmetric Function.
  • a Symmetric Operation.
  • Vector Addition Commutativity Axiom: ∀v,w∈V, v + w = w + v.
• See: Anticommutativity Property, Vector Space, Associativity Property, Distributivity Property,----

References

• (WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=commutative
  • (of a binary operation) independent of order; as in e.g. “a x b = b x a"
• http://en.wiktionary.org/wiki/commutative
  • Adjective
    • 1. (algebra) (of an operator * ) such that, for any operands a,b, a * b = b * a
    • 2. (algebra) Having a commutative operation.
• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Commutativity
  • In mathematics, commutativity is the property that changing the order of something does not change the end result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. The commutativity of simple operations, such as multiplication and addition of numbers, was for many years implicitly assumed and the property was not named until the 19th century when mathematicians began to formalize the theory of mathematics.

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