Definition (Function) RC A x B is a function from A to B if a∈A:3b∈B:(a,b)∈f: For Proof: Va∈A: a∈A:3b∈B:(a,b)∈f 3b∈B: ∀b,b∈B:(a,b)∈f∧(a,b)∈f→b=b Hengfeng Wei (hfweiinju.edu.cn)1-10 Set Theory (III):Functions 2019年12月10日7/40Definition (Function) R ⊆ A × B is a function from A to B if ∀a ∈ A : ∃!b ∈ B : (a, b) ∈ f. For Proof: ∀a ∈ A : ∀a ∈ A : ∃b ∈ B : (a, b) ∈ f ∃!b ∈ B : ∀b, b′ ∈ B : (a, b) ∈ f ∧ (a, b′ ) ∈ f =⇒ b = b ′ Hengfeng Wei (hfwei@nju.edu.cn) 1-10 Set Theory (III): Functions 2019 年 12 月 10 日 7 / 40