Bounded sequence implies convergent subsequence

  • #1
Scousergirl
16
0
How can you deduce that nad bounded sequence in R has a convergent subsequence?
 

Answers and Replies

  • #2
morphism
Science Advisor
Homework Helper
2,017
4
This is the Bolzano–Weierstrass theorem. Any decent calculus or analysis textbook should have a proof of it. Or search online. Or use this hint: Prove that a bounded sequence of real numbers has a monotone subsequence.
 

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