This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: i=1 A i = {0}. c) As I increases, the sets get larger: A 1 2 A 3 .. . All the sets are subsets of the set of positive real numbers R + , and every positive real number is included eventually, so U i=1 A i =R + . Because A 1 is a subset of each of the others, i=1 A i = A 1 = (0,1) (tne interval of all real numbers between 0 and 1, exclusive). d) This time , as in part (a), the sets are getting smaller as i increase:. A 3 2 A 1 . Because A 1 includes all the others, U i=1 A i = (1, ) (all real numbers greater than 1). Every number eventually gets excluded as I increases, so i=1 A i = ] . Notice that is not a real number, so we cannot write i=1 A i ={} 50. 001110 0000...
View Full
Document
 Spring '09

Click to edit the document details