Subsequences and Bolzano-Weierstrass theorem
General · Mathematics
Study notes
Q: Find convergent subsequences of (-1)ⁿ and of sin(n). State Bolzano-Weierstrass. (-1)ⁿ: even terms → 1; odd terms → -1 (both converge!). B-W: every BOUNDED sequence has a convergent subsequence! sin(n): bounded (in [-1,1]) → some subsequence converges (limit unknown, exists!). Unbounded n²: no convergent subsequence!