However, if A 0 ∩ A 1 ≠ ∅ {\displaystyle A_{0}\cap A_{1}\neq \emptyset } , then f {\displaystyle f} would not be well defined because f ( a ) {\displaystyle f(a)} is "ambiguous" for a ∈ A 0 ∩ A 1 {\displaystyle a\in A_{0}\cap A_{1}} . For example, if A 0 := { 2 } {\displaystyle A_{0}:=\{2\}} and A 1 := { 2 } {\displaystyle A_{1}:=\{2\}} , then f ( 2 ) {\displaystyle f(2)} would have to be both 0 and 1, which makes it ambiguous. As a result, the latter f {\displaystyle f} is not well defined and thus not a function.