f:A→B 9:C→D Q:Is fug a function? Theorem (Union of Functions) fUg:(AUC)→(BUD)←→a∈dom(f)∩dom(g):f(x)=g(x) UD Problem 14.3 (g) f:Q→R x+1fx∈2Z f(x)= x-1 ifx∈3Z 2 otherwise x∈6Z Hengfeng Wei (hfweixinju.edu.cn) 1-10 Set Theory (III):Functions 2019年12月10日15/40f : A → B g : C → D Q : Is f ∪ g a function? Theorem (Union of Functions) f ∪ g : (A ∪ C) → (B ∪ D) ⇐⇒ ∀x ∈ dom(f) ∩ dom(g) : f(x) = g(x) UD Problem 14.3 (g) f : Q → R f(x) =    x + 1 if x ∈ 2Z x − 1 if x ∈ 3Z 2 otherwise x ∈ 6Z Hengfeng Wei (hfwei@nju.edu.cn) 1-10 Set Theory (III): Functions 2019 年 12 月 10 日 15 / 40