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Let K1 ⊃ K2 ⊃ K3 ⊃ ... be a sequence of bounded closed sets. Let...

Let K1 ⊃ K2 ⊃ K3 ⊃ ... be a sequence of bounded closed sets. Let (an) be a sequence of numbers with the property an ∈ Kn \ Kn+1. Show that (an) has a subsequence that converges to a point a ∈ ??Kn. Carefully state which theorems you are using.

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Given: kokzokz0.... Bounded & closed e an E kn .kntl. {an} sequence To prove Il a subsequence of {an} that Converges to a Enclassmate Date Page ompakt k closed & Bounded Bolzano Weiersteass theorem: Closed & Bounded 2 Sequentially » Kib SequentiallyConsider a subsequence of Sank} (San such that fan 3 e ke nt ( leaving the first and where met Иe 0 Now, şan? is also a subse

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