Definition(Ordered Pairs (Kazimierz Kuratowski;1921)) (a,b){a},{a,b} Theorem (a,b)=(c,d→a=c∧b=d Proof. {ah,{a,b}={c,{c,d} 4口，1①，43，t夏，30Q0 Jun iE jtmomjtedn.cn 1-9 Set Theory (II):Relations 2021 1202 5/52. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition (Ordered Pairs (Kazimierz Kuratowski; 1921)) (a, b) , { {a}, {a, b} } Theorem (a, b) = (c, d) ⇐⇒ a = c ∧ b = d Proof. { {a}, {a, b} } = { {c}, {c, d} } Case I : a = b Case II : a ̸= b Jun Ma (majun@nju.edu.cn) 1-9 Set Theory (II): Relations 2021 年 12 月 02 日 5 / 52