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math104-s22:s:jonathanwang

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math104-s22:s:jonathanwang [2022/01/31 21:44]
192.31.105.170 [Questions] 		math104-s22:s:jonathanwang [2026/02/21 14:41] (current)
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 ====== Questions  ====== ====== Questions  ======
-For 11.2.ii, why does $s_{n_k}$ need to be greater than $\max\{s_{n_{k-1}}, k\}$ instead of just $s_{n_{k-1}}$?+1. For 11.2.ii in Ross, why does $s_{n_k}$ need to be greater than $\max\{s_{n_{k-1}}, k\}$ instead of just $s_{n_{k-1}}$? 
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 +2. Why is 1(7) in [[https://courses.wikinana.org/_media/math104-f21/math_104-mt1.pdf]] false? I thought one could argue $|a_m - a_n| < \sum \tilde{\epsilon} < \epsilon$ 
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 +3. Why is 1(9) in [[https://courses.wikinana.org/_media/math104-f21/math_104-mt1.pdf]] false? 
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 +4. In Cantor's diagonalization argument, is the reason we can't take the sequence straight downwards because there may be repeated elements? 
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 +5. When Prof Zhou showed Cantor's diagonalization argument on 2/15, he produced a monotonically decreasing subsequence. However, I thought in general, although each sequence has a monotonic subsequence, it could be either increasing or decreasing. Thus, was the choice of monotonically decreasing just WLOG?
math104-s22/s/jonathanwang.1643665463.txt.gz · Last modified: 2026/02/21 14:43 (external edit)

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