Then f {\displaystyle f} is well defined if A 0 ∩ A 1 = ∅ {\displaystyle A_{0}\cap A_{1}=\emptyset \!} . For example, if A 0 := { 2 , 4 } {\displaystyle A_{0}:=\{2,4\}} and A 1 := { 3 , 5 } {\displaystyle A_{1}:=\{3,5\}} , then f ( a ) {\displaystyle f(a)} would be well defined and equal to mod ⁡ ( a , 2 ) {\displaystyle \operatorname {mod} (a,2)} .