Editing Well-defined expression (section)

==Well-defined notation==
For real numbers, the product <math>a \times b \times c</math> is unambiguous because <math>(a \times b)\times c = a \times (b \times c)</math>; hence the notation is said to be ''well defined''.<ref name="MathWorld"/> 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 <math>a-b-c</math> is shorthand for <math>(a-b)-c</math>, thus it is considered "well-defined". On the other hand, [[Division (mathematics)|Division]] is non-associative, and in the case of <math>a/b/c</math>, parenthesization conventions are not well established; therefore, this expression is often considered ill-defined.

Unlike with functions, notational ambiguities can be overcome by means of additional definitions (e.g., rules of [[Operator precedence|precedence]], associativity of the operator). For example, in the programming language [[C (programming language)|C]], the operator <code>-</code> for subtraction is ''left-to-right-associative'', which means that <code>a-b-c</code> is defined as <code>(a-b)-c</code>, and the operator <code>=</code> for assignment is ''right-to-left-associative'', which means that <code>a=b=c</code> is defined as <code>a=(b=c)</code>.<ref>{{Cite web|url=https://www.geeksforgeeks.org/operator-precedence-and-associativity-in-c/|title=Operator Precedence and Associativity in C|date=2014-02-07|website=GeeksforGeeks|language=en-US|access-date=2019-10-18}}</ref> In the programming language [[APL (programming language)|APL]] there is only one rule: from [[APL (programming language)#Design|right to left]] – but parentheses first.