Well-defined

Well-defined notation

For real numbers, the product ${\displaystyle a\times b\times c}$ is unambiguous because ${\displaystyle (a\times b)\times c=a\times (b\times c)}$; hence the notation is said to be well defined. This property, also known as associativity of multiplication, guarantees the result does not depend on the sequence of multiplications; therefore, a specification of the sequence can be omitted. The subtraction operation is non-associative; despite that, there is a convention that ${\displaystyle a-b-c}$ is shorthand for ${\displaystyle (a-b)-c}$, thus it is considered "well-defined". On the other hand, division is non-associative, and in the case of ${\displaystyle a/b/c}$, parenthesization conventions are not well established; therefore, this expression is often considered ill-defined.