Wildcat
Apr27-11, 08:24 PM
{xn} is an infinite sequence and xi ≠ xj if i ≠j. Let A and B denote all finite subsequences of {xn} and all infinite subsequences of {xn}, respectively.
Show that B ≈ (0,1).
2. Relevant equations
3. The attempt at a solution
Using binary expansion, given a from (0,1) we have a=0.a1a2a3... where ai is either 0 or 1. You can map a to a subsequence which consists of those xi whose corresponding ai=1 where do I go from here???
Show that B ≈ (0,1).
2. Relevant equations
3. The attempt at a solution
Using binary expansion, given a from (0,1) we have a=0.a1a2a3... where ai is either 0 or 1. You can map a to a subsequence which consists of those xi whose corresponding ai=1 where do I go from here???