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--- math104-s22:notes:lecture_2 [2022/01/19 10:10]
pzhou
+++ math104-s22:notes:lecture_2 [2022/01/19 10:13] (current)
pzhou [Group Discussion (20min)]
@@ Line 20: / Line 20: @@
 . Let  $A, B \In \R$ , and define  $A+B = \{a + b| a \in A, b \in B \}$ . Prove that  $\sup (A+B) = \sup A + \sup B$ .
-. Let  $A$  be a subset of  $\R$ , what's the difference between $\sup A $and$ \max A$? (Read Ross Sec 3, if in doubt)
+. Same setup as above, prove that $\sup (A \cup B) = \max(\sup A, \sup B) $.
-. Can you prove using definition that,  $\lim_n \frac{2n+1}{3n-1} = 2/3$ ? (hint, divide both numerator and denominator by  $n$ )
+. Ross 7.1, 7.2, 7.3
+{{:math104-s22:notes:pasted:20220119-101341.png}}

Lecture Notes