stylistic:tone, linguistic:voice_change, linguistic:paraphrasing
Expressions

An expression is a finite combination of symbols that is well-formed according to rules that depend on the context. In general, an expression denotes or names a mathematical object, and plays therefore in the language of mathematics the role of a noun phrase in the natural language.

An expression contains often some operators, and may therefore be evaluated by the action of the operators in it. For example, 3 + 2 {\displaystyle 3+2} is an expression in which the operator + {\displaystyle +} can be evaluated for giving the result 5. {\displaystyle 5.} So, 3 + 2 {\displaystyle 3+2} and 5 {\displaystyle 5} are two different expressions that represent the same number. This is the meaning of the equality 3 + 2 = 5. {\displaystyle 3+2=5.}

A more complicated example is given by the expression ∫ a b x d x {\textstyle \int _{a}^{b}xdx} that can be evaluated to b 2 2 − a 2 2. {\textstyle {\frac {b^{2}}{2}}-{\frac {a^{2}}{2}}.} Although the resulting expression contains the operators of division, subtraction and exponentiation, it cannot be evaluated further because a and b denote unspecified numbers.