Thread: Proving Divergence

The definition of a convergent squence is:
For every L in Real numbers, and all E>0 such that there exists N in Natural numbers n>/= N implies |xn-L|>E.
Negate this statement then use the negation to prove that the sequence xn=(-1)^n is not convergent.

I got the negation I think, but I'm not sure how to begin with the proof. We went over one example in class and it was for proving something converges. I got the negation as :
For all L in real numbers, there exists E>0 such that there exits N in natural numbers and n>/=N implies |xn-L|<E

Your definition of convergence is not correct. It should be

There exists L in Real numbers such that for all E>0 such that there exists N in Natural numbers such that n>/= N implies |xn-L|< E.

The negation of the definition of convergence should be: For every real number there exists a real number such that for every natural number there is a natural number such that Use this to prove the divergence of where Hint: Given let if and if

I don't understand how you are proving the negation. We just used the pieces of the definition to prove convergence in class. Is that what you are doing here?

Originally Posted by renolovexoxo

I don't understand how you are proving the negation. We just used the pieces of the definition to prove convergence in class. Is that what you are doing here?

Is this true:
If that is true, how can the terms of the sequence get "close together"?

I'm getting lost. I feel like there is something there that I'm not understanding.

Originally Posted by renolovexoxo

I'm getting lost. I feel like there is something there that I'm not understanding.

I think that you need a live-sit-down with an instructor/lecturer.
We here just not equipped to aid with this kind profound confusion.
Talk to your instructor!

I can't or I would. Thanks for trying I suppose. I understand the second piece, but between the first response and the first line of what you wrote I can't figure it out. Do I only need the fact that they cannot equal 2 or get closer together for all n? That's really where I'm getting hung up. If asked to explain it, I could, it's more where I am supposed to get this fact from that is causing an issue. Should I just have been able to know that?