math104-s22:notes:lecture_2
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math104-s22:notes:lecture_2 [2022/01/19 18:10] pzhou |
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| 1. Let $A, B \In \R$, and define $A+B = \{a + b| a \in A, b \in B \}$. Prove that $\sup (A+B) = \sup A + \sup B$. | 1. Let $A, B \In \R$, and define $A+B = \{a + b| a \in A, b \in B \}$. Prove that $\sup (A+B) = \sup A + \sup B$. | ||
| - | 2. Let $A$ be a subset of $\R$, what's the difference between | + | 2. Same setup as above, prove that $\sup (A \cup B) = \max(\sup A, \sup B) $. |
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| - | 3. Can you prove using definition that, $\lim_n \frac{2n+1}{3n-1} = 2/3$? (hint, divide both numerator and denominator by $n$) | + | |
| + | 3. Ross 7.1, 7.2, 7.3 | ||
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math104-s22/notes/lecture_2.1642615843.txt.gz · Last modified: 2026/02/21 14:44 (external edit)
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