1. (10 pts) There is a reason all our definitions in this class begin with Ve > 0. Here are two results which can be con
Posted: Tue Sep 07, 2021 7:37 am
- 1 10 Pts There Is A Reason All Our Definitions In This Class Begin With Ve 0 Here Are Two Results Which Can Be Con 1 (16.5 KiB) Viewed 67 times
1. (10 pts) There is a reason all our definitions in this class begin with Ve > 0. Here are two results which can be considered two sides of the same concept - I consider it the fundamental observation of analysis - which is the reason for this ubiquity of Ve > 0. Prove both separately. (a) (5 pts) Let c be a nonnegative number, i.e. c> 0. Suppose ce for all e > 0. Prove that c= 0. (b) (5 pts) Let a,b be real numbers so that a 6. Prove there is an e > 0 so that for all 3 € R, if c-al <e then I b.