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--- math104-s21:hw3 [2021/02/06 09:19]
pzhou
+++ math104-s21:hw3 [2026/02/21 14:41] (current)
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-====== HW3 ======
+====== HW 3 ======
 In this week, we finished section 10 on monotone sequence and Cauchy sequence, and also touches a bit on constructing subsequences. It is important to understand the statements of the propositions/theorems that we talked about in class, and then try to prove them yourselves, then compare with notes and textbook.
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 . 10.11
-. Let $S$ be the subset of $(0,1)$ where $x \in S$ if and only if $x$ has a finite decimal expression $0.a_1 a_2 \cdots a_n$ for some $n$, and the last digit $a_n=3$. Show that for any $t \in (0,1)$ and any $\epsilon >0$, there is a sequence $s_n$ in S that converges to $t$.
+. Let $S$ be the subset of $(0,1)$ where $x \in S$ if and only if $x$ has a finite decimal expression $0.a_1 a_2 \cdots a_n$ for some $n$, and the last digit $a_n=3$. Show that for any $t \in (0,1)$, there is a sequence $s_n$ in S that converges to $t$.

Lecture Notes