a) Suppose that and converge to the same point. Prove that as .
b) Show the converse is false.
Again as usual... some kind of explanation to help me understand this helps alot...
I finished part a). Thanks for the help. Now about part b). First what exactly would the converse be? I know its If X then Y becomes If Y then X. I was thinking maybe by showing something like subtraction is not commutative. Like if X - Y 0 is not the same as Y - X 0.
The answer is no, the limit must be the same for both sequences.
Suppose that .
That means that almost all the terms of are ‘close’ to ; almost all the terms of are ‘close’ to ; and almost all the terms of are ‘close’ to .
Suppose then .
But how can almost all of the three sequences be with in an -distance of its limit?