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--- math104-s21:hw3 [2021/02/06 01:19]
pzhou
+++ math104-s21:hw3 [2022/01/11 10:57] (current)
pzhou ↷ Page moved from math104-2021sp:hw3 to math104-s21:hw3
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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