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你们好。 在下有谁可以教我怎么做这3道集合论习题吗？
感谢。
1. Let x, y, z be sets.
设x,y,x是集合.
(a) Show that, with the definition above, (x, y, z) is a unique set.
证明 (x, y, z)是唯一集合.
(b) Show that if u, v, w are sets with (x, y, z) = (u, V , w), then x = u, y = v and z = W.
证明如果 (x, y, z) = (u, v, w), 于是 x = u, y = v and z = w。
2. Show that {x, {y}} is not suitable as a definition of the ordered pair (x, y), because it does not have the ordered pair property (as in Theorem 4.2).
Theorem 4.2 The ordered pair property
For any sets x, y, u, v, if (x, y ) = (u, v), then x = u and y = v.
题目是 D. C. Goldrei 的 Classic Set Theory: For Guided Independent Study 书里得到的。
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