Macroeconomics Exam Review 10

Macroeconomics Exam Review 10 - ( , ) ( , ) Figure 1.3: A...

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Unformatted text preview: ( , ) ( , ) Figure 1.3: A convergent sequence cannot have two distinct limits 1.98 The share of the th guest is = 1 2 lim = 0 However, > 0 for all . There is no limit to the number of guests who will get a share of the cake, although the shares will get vanishingly small for large parties. 1.99 Suppose . That is, there exists some such that ( , ) < / 2 for all . Then, for all , ( , ) ( , ) + ( , ) < / 2 + / 2 = 1.100 Let ( ) be a Cauchy sequence. There exists some such that ( ) < 1 for all . Let = max { ( 1 ) , ( 2 ) ,..., ( 1 ) , 1 } Every belongs to ( , + 1), the ball of radius...
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