# 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 takes real numbers as input, and if does not equal then 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 , then even though is undefined does not mean that the function is *not* well defined – but simply that 0 is not in the domain of .