Solution 17.

See text and/or instructor's solution manual.

Solution.   Let      and suppose   .   

This means there exists and    such that    implies that  ,  that is,  .  

But then   ,   so also we have   ,   for all   .  

Therefore,   .   

      The other direction is similar.   Let      and suppose   .   

This means there exists and    such that    implies that   .

But then  ,   so also we have   ,   for all   .      

Therefore,    .   

This solution is complements of the authors.

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