# Expression (mathematics)

## A finite combination of symbols that describes a mathematical object / From Wikipedia, the free encyclopedia

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In mathematics, an **expression** is a written arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can denote numbers (constants), variables, operations, functions. Other symbols include punctuation signs and brackets (often used for grouping, that is for considering a part of the expression as a single symbol).

Many authors distinguish an expression from a *formula*, the former denoting a mathematical object, and the latter denoting a statement about mathematical objects.^{[1]} This is analogous to natural language, where a noun phrase refers to an object, and a whole sentence refers to a fact. For example, $8x-5$ is an expression, while $8x-5\geq 3$ is a formula.

Expressions can be *evaluated* or *partially evaluated* by replacing operations that appear in them with their result. For example, the expression $8\times 2-5$ evaluates partially to $16-5$ and totally to $11.$

An expression is often used to define a function, by taking the variables to be arguments, or inputs, of the function, and assigning the output to be the total evaluation of the resulting expression.^{[2]} For example, $x\mapsto x^{2}+1$ and $f(x)=x^{2}+1$ define the function that associates to each number its square plus one. An expression with no variables would define a constant function.