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... :)

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- Oct 26th 2008, 02:21 PMCaitySequence Convergence proof maybe?
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... :) - Oct 26th 2008, 02:57 PMwhipflip15
For part a) i would use the definition of limits and it should follow directly. For part b) you just need to show a counter example. Maybe look at

- Oct 27th 2008, 05:28 AMCaity
ok that was how I started it... thanks for the info...

- Oct 27th 2008, 07:02 AMPlato
- Oct 27th 2008, 11:01 AMCaity
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.

- Oct 27th 2008, 12:43 PMPlato
The converse is: Suppose that the & have the same limit.

- Oct 28th 2008, 07:38 AMCaity
- Oct 28th 2008, 09:01 AMPlato
Try this counterexample.

Note: we are not given that the sequences converge, only that their difference is null. - Oct 30th 2008, 11:51 AMMoo
- Oct 30th 2008, 12:39 PMPlato
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?