- #1
playa007
- 29
- 0
Homework Statement
Suppose {a_n} is a bounded sequence who's set of all subsequential
limits points is {0,1}. Prove that there exists two subsequences,
such that: one subsequence converges to 1 while the other converges
to 0, and each a_n belongs to exactly one of these subsequences.
Homework Equations
The Attempt at a Solution
Well, it's clear that at the limit points 0 and 1; there is a subsequence that that converges to it. I'm not quite sure about how to prove that each a_n belongs to exactly one of these subsequences or how to apply the bounded property of {a_n} into this question.