Some Basic Properties of Sets 论文

摘要

In this paper x, x1, x2, y, y1, y2, z, A, B, X , X1, X2, X3, X4, Y , Y1, Y2, Z, N, M denote sets. Let x, y be sets. One can verify that 〈x, y〉 is non empty. Let us consider X . The functor 2X is defined by: (Def. 1) Z ∈ 2X iff Z ⊆ X . Let us consider X1, X2. The functor [:X1, X2 :] is defined as follows: (Def. 2) z ∈ [:X1, X2 :] iff there exist x, y such that x ∈ X1 and y ∈ X2 and z = 〈x, y〉. Let us consider X1, X2, X3. The functor [:X1, X2, X3 :] is defined by: (Def. 3) [:X1, X2, X3 :] = [: [:X1, X2 :], X3 :]. Let us consider X1, X2, X3, X4. The functor [:X1, X2, X3, X4 :] is defined by: (Def. 4) [:X1, X2, X3, X4 :] = [: [:X1, X2, X3 :], X4 :].