The Bolzano-Weierstrass theorem asserts, under appropriate circumstances, the convergence of some subsequence of a sequence. While this famous theorem ignores the actual limit of the subsequence, it is natural to investigate such limits. This note characterizes the set of possible limits of subsequences of a given sequence.
Copyright © 2008 Mathematical Association of America. All rights reserved. NOTICE: This is the author’s version of a work that was accepted for publication in Mathematics Magazine 81(5): 369-373. A definitive version can be viewed at: http://www.jstor.org/stable/27643144
Sibley TQ. 2008. Sublimital Analysis. Mathematics Magazine 81(5): 369-373.