math104-f21:hw2
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math104-f21:hw2 [2021/09/03 05:04] pzhou created |
math104-f21:hw2 [2026/02/21 14:41] (current) |
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| ====== HW 2 ====== | ====== HW 2 ====== | ||
| - | Due Tuesday | + | Due Thursday |
| In the following, a sequence $(a_n)$ means $(a_n)_{n=0}^\infty$, | In the following, a sequence $(a_n)$ means $(a_n)_{n=0}^\infty$, | ||
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| 3. Let $(a_n)$ be a Cauchy sequence in $\Q$, and let the sequence $(b_n)$ be defined such that $b_n = a_{2n}$. | 3. Let $(a_n)$ be a Cauchy sequence in $\Q$, and let the sequence $(b_n)$ be defined such that $b_n = a_{2n}$. | ||
| - | 4. Tao p115, Exercise 5.4.1 | + | 4. If $(a_n)$ and $(b_n)$ are Cauchy sequences, prove that $(a_n b_n)$ is also a Cauchy sequence. |
| - | 5. Tao p116. Exercise | + | 5. If $(a_n)$, $(c_n)$ and $(b_n)$ are Cauchy sequences, and $(a_n) \sim (c_n)$, prove that $(a_n b_n) \sim (c_n b_n)$. |
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| + | (Problem 4 and 5 together proves Tao proposition | ||
math104-f21/hw2.1630645452.txt.gz · Last modified: 2026/02/21 14:43 (external edit)
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