第3章 章节3.2 练习3.2.4 题目： How many elements does \( S_3 \) have? 解答： 根据\( S_{i + 1} \)的定义，\( |S_{i + 1}| = 3 + 3|S_i| + |S_i|^3 \)，于是从\( |S_0| = 0 \)开始慢慢

第2章 章节2.2 练习2.2.6 题目： Suppose we are given a relation \( R \) on a set \( S \). Define the relation \( R' \) as follows: \[ R' = R \cup \{ (s, s) \mid s \in S \} \text{.} \] That is, \( R' \) contains all the pairs in \( R \) plus

前言 我看了多本数学分析、微积分的书，陶哲轩的Analysis I是唯一一本把动机讲清楚的（且非常重视动机），同时作者会特别注意避免后向引用，即

附录B 版本 Analysis I（第3版）。 章节B.1 练习B.1.1 题目： The purpose of this exercise is to demonstrate that the procedure of long addition taught to you in elementary school is actually valid. Let \( A = a_n \dots a_0 \) and \( B = b_m \dots b_0 \) be positive integer

附录A 版本 Analysis I（第3版）。 章节A.1 练习A.1.1 题目： What is the negation of the statement “either X is true, or Y is true, but not both”? 解答： 命题“要么\( X \)为真，要么\( Y \)为

第11章 版本 Analysis I（第3版）。 章节11.1 练习11.1.1 题目： Prove Lemma 11.1.4. (Hint: in order to show that 1 implies 2 in the case when \( X \) is non-empty, consider the supremum and infimum of \( X \).) Lemma 11.1.4的内