Mathematical terminology

Well-defined expression

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. 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). 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) = 1/x, then the fact that f(0) is undefined does not mean that the f is not well defined – but that 0 is simply not in the domain of f. (Wikipedia).

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Division (mathematics) | Binary relation | Expression (mathematics) | Domain of a function | Mathematics | Operation (mathematics) | Undefined (mathematics) | Modulo operation | Well-formed formula | Subtraction | Coset | Partial differential equation | Cartesian product | Modular arithmetic | Uniqueness quantification