# Well-defined expression

## Expression whose definition assigns it a unique interpretation / From Wikipedia, the free encyclopedia

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In mathematics, a **well-defined expression** or **unambiguous expression** is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be *not well defined*, **ill defined** or *ambiguous*.^{[1]} A function is well defined if it gives the same result when the representation of the input is changed without changing the value of the input. For instance, if $f$ takes real numbers as input, and if $f(0.5)$ does not equal $f(1/2)$ then $f$ is not well defined (and thus not a function).^{[2]} The term *well-defined* can also be used to indicate that a logical expression is unambiguous or uncontradictory.

A function that is not well defined is not the same as a function that is undefined. For example, if $f(x)={\frac {1}{x}}$, then even though $f(0)$ is undefined, this does not mean that the function is *not* well defined; rather, 0 is not in the domain of $f$.