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Oct2-08, 07:17 PM
HW Helper
P: 2,264
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
Contains all but a finite number of the a_n
now the sequence can be easily partitioned by
one subsequence if a_n<=1/2
another if a_n>1/2