3 x 4 is the same as the 4 x 3 and 3 + 4 is the same as 4
+ 3. But 3 ÷ 4 is not the same as 4 ÷ 3 and
3 - 4 is not the same as 4 - 3. Multiplication and addition
of numbers are said to be commutative. Division and subtraction
of numbers are not commutative (non-commutative).
In mathematics, commutativity is the ability to change the
order of something without changing the end result. It is
a fundamental property in most branches of mathematics and
many proofs depend on it. The commutativity of simple operations
was for many years implicitly assumed and the property was
not given a name or attributed until the 19th century when
mathematicians began to formalize the theory of mathematics.
An operation x on a set is commutative when it does not matter
which way round two elements in the set are combined, i.e.,
when a x b = b x a for all elements a and b in the set.