Well-defined expression

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a well-defined expression or unambiguous expression is an <a href="/facts/Expression_(mathematics)/MPrMlYbE">expression</a> 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
 
 
 {\displaystyle f}
 
 takes real numbers as input, and if 
 
 
 
 f
 (
 0.5
 )
 
 
 {\displaystyle f(0.5)}
 
 does not equal 
 
 
 
 f
 (
 1
 
 /
 
 2
 )
 
 
 {\displaystyle f(1/2)}
 
 then 
 
 
 
 f
 
 
 {\displaystyle 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 <a href="/facts/Undefined_(mathematics)/Bc1Q3px4">undefined</a>. For example, if 
 
 
 
 f
 (
 x
 )
 =
 
 
 1
 x
 
 
 
 
 {\displaystyle f(x)={\frac {1}{x}}}
 
, then even though 
 
 
 
 f
 (
 0
 )
 
 
 {\displaystyle f(0)}
 
 is undefined, this does not mean that the function is not well defined; rather, 0 is not in the <a href="/facts/Domain_of_a_function/FQvoeUpX">domain</a> of 
 
 
 
 f
 
 
 {\displaystyle f}
 
.

Well-defined expression open-in-new

Well-defined expression