Editing Mathematical notation (section)

== Expressions and formulas ==
An expression is a written arrangement of [[Symbol (mathematics)|symbols]] following the context-dependent, [[Syntax (logic)|syntactic]] conventions of mathematical notation. Symbols can denote [[numbers]], [[Variable (mathematics)|variables]], [[Operation (mathematics)|operations]], and [[Function (mathematics)|functions]].<ref>[[Oxford English Dictionary]], s.v. “[[doi:10.1093/OED/4555505636|Expression (n.), sense II.7]],” "''A group of symbols which together represent a numeric, algebraic, or other mathematical quantity or function.''"</ref> Other symbols include [[punctuation]] marks and [[Bracket (mathematics)|brackets]], used for [[Symbols of grouping|grouping]] where there is not a well-defined [[order of operations]].

Expressions are commonly distinguished from ''[[Mathematical formula|formulas]]'': expressions are a kind of [[mathematical object]], whereas formulas are statements ''about'' mathematical objects.<ref>{{cite book |last=Stoll |first=Robert R. |title=Set Theory and Logic |publisher=Dover Publications |year=1963 |isbn=978-0-486-63829-4 |location=San Francisco, CA}}</ref> This is analogous to [[natural language]], where a [[noun phrase]] refers to an object, and a whole [[Sentence (linguistics)|sentence]] refers to a [[fact]]. For example, <math>8x-5</math> is an expression, while the [[Inequality (mathematics)|inequality]] <math>8x-5 \geq 3 </math> is a formula.

To ''evaluate'' an expression means to find a numerical [[Value (mathematics)|value]] equivalent to the expression.<ref>[[Oxford English Dictionary]], s.v. "[[doi:10.1093/OED/3423541985|Evaluate (v.), sense a]]", "''Mathematics. To work out the ‘value’ of (a quantitative expression); to find a numerical expression for (any quantitative fact or relation).''"</ref><ref>[[Oxford English Dictionary]], s.v. “[[doi:10.1093/OED/1018661347|Simplify (v.), sense 4.a]]”, "''To express (an equation or other mathematical expression) in a form that is easier to understand, analyse, or work with, e.g. by collecting like terms or substituting variables.''"</ref> Expressions can be ''evaluated'' or ''simplified'' by replacing [[Operation (mathematics)|operations]] that appear in them with their result. For example, the expression <math>8\times 2-5</math> simplifies to <math>16-5</math>, and evaluates to <math>11.</math>