Editing Expression (mathematics) (section)

=== Well-formed ===
The syntax of mathematical expressions can be described somewhat informally as follows: the allowed [[operator (mathematics)|operator]]s must have the correct number of inputs in the correct places (usually written with [[infix notation]]), the sub-expressions that make up these inputs must be well-formed themselves, have a clear [[order of operations]], etc. Strings of symbols that conform to the rules of syntax are called [[Well-formedness|''well-formed'']], and those that are not well-formed are called, ''ill-formed'', and do not constitute mathematical expressions.<ref>{{cite book |last=Stoll |first=Robert R. |title=Set Theory and Logic |publisher=Dover Publications |isbn=978-0-486-63829-4 |location=San Francisco, CA |year=1963}}</ref>

For example, in [[arithmetic]], the expression ''1 + 2 × 3'' is well-formed, but  
:<math>\times4)x+,/y</math>.
is not.

However, being well-formed is not enough to be considered well-defined. For example in arithmetic, the expression <math display="inline">\frac{1}{0}</math> is well-formed, but it is not well-defined. (See [[Division by zero]]). Such expressions are called [[Undefined (mathematics)|undefined]].