Kinds of uniqueness
DefinitionsSay we define a value by giving a condition that must hold on it. Then we say:
is unique if the condition determines at most one value. Mathematically, we consider to be unique if for all satisfying we have that
Define to be the value such that . Then is not unique, since both and satisfy this condition.
Define to be the value such that and . Then is unique and is given by
Define to be the 0-element set. Then is unique and is given by .