How can you deduce that nad bounded sequence in R has a convergent subsequence?
Sep 19, 2007 #1 Scousergirl 16 0 How can you deduce that nad bounded sequence in R has a convergent subsequence?
Sep 19, 2007 #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.
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.