Exercise 19.  Use the definition in Exercise 9 to prove that  .  

Solution 19.

See text and/or instructor's solution manual.

Solution.  Let    be given.   

Choose  .  

Assume  .  

Then  .  

Therefore  ,  so  .  

Therefore,  .

change the following idea for this problem
Then  ,  so  ,  i.e.,  .

(To see how we got  R,  start with  , and work backwards in the above steps.)

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell