and be sure that the value of does not depend on that choice (this is justified in the entry fraction power). So, the is well-defined.
In many instances well-defined is a synonym for the formal definition of a function between sets. For example, the function is a well-defined function from the real numbers to the real numbers because every input, , is assigned to precisely one output, . However, is not well-defined in that one input can be assigned any one of two possible outputs, or .
More subtle examples include expressions such as
Certainly every input has an output, for instance, . However, the expression is not well-defined since yet while and .
One must question whether a function is well-defined whenever it is defined on a domain of equivalence classes in such a manner that each output is determined for a representative of each equivalence class. For example, the function was defined using the representative of the equivalence class of fractions equivalent to .
|Date of creation||2013-03-22 17:31:32|
|Last modified on||2013-03-22 17:31:32|
|Last modified by||pahio (2872)|