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Unformatted text preview: ) . ) ∞ 4 . Let ( a n n =1 be a sequence in R with the property that no subsequence converges. Prove that  a n  → ∞ . Does the same property hold if the a n are in Q and we consider ( a n ) ∞ n =1 as a sequence in the metric space Q ? MIT OpenCourseWare http://ocw.mit.edu 18.100B Analysis I Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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This document was uploaded on 10/26/2011 for the course MATH 18.100B at MIT.
 Fall '10
 Prof.KatrinWehrheim
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