Let A 0 , A 1 {\displaystyle A_{0},A_{1}} be sets, let A = A 0 ∪ A 1 {\displaystyle A=A_{0}\cup A_{1}} and "define" f : A → { 0 , 1 } {\displaystyle f:A\rightarrow \{0,1\}} as f ( a ) = 0 {\displaystyle f(a)=0} if a ∈ A 0 {\displaystyle a\in A_{0}} and f ( a ) = 1 {\displaystyle f(a)=1} if a ∈ A 1 {\displaystyle a\in A_{1}} .