Question

Let {an} be a sequence. Let {bnk} and {cnk} be subsequences of {an}. Prove directlythat if {bnk} converges to b and {cnk}converges to c with b =/= c, then {an} does not converge to c

Answer 1

My connection has been pretty poor with open study just fyi.

I think I could do a proof by contradiction, but specifying that its a direct proof has me not sure of how to go about it.

Answer 2

I am not too good with proofs, but I believe the correct approach would be to prove that a sequence can not converge, if its sub-sequences converge to different limits

Answer 3

http://astarmathsandphysics.com/university-maths-notes/analysis/university-maths-notes-analysis-subsequences.html

Answer 4

check out that link

Answer 5

http://math.stackexchange.com/questions/382943/subsequence-proof