Thread: Subsequential limit question View Single Post
 HW Helper P: 2,263 This will depend slightly on the definition you are using. Suppose {a_n} is a bounded sequence who's set of all subsequential limits points is {0,1} Suppose epps is a positive real number 0 and one are limit points so it is known that (-eps,eps)U(1-eps,1+eps) Contains all but a finite number of the a_n now the sequence can be easily partitioned by 1/2 one subsequence if a_n<=1/2 another if a_n>1/2