Prove lim(x sub n) = 0 if and only if lim(|x sub n|)= 0.

I am not sure how to even start this or what property of limits apply here.

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- Oct 10th 2008, 03:46 PMhayter221Limit Proof
Prove lim(x sub n) = 0 if and only if lim(|x sub n|)= 0.

I am not sure how to even start this or what property of limits apply here. - Oct 10th 2008, 04:06 PMPlato
- Oct 10th 2008, 07:40 PMhayter221
Can you show me how to incorporate this into the proof? I have that for every epsilon>0 there exists a natural number K(epsilon) such that for all n>or equal to K(epsilon) the tems x sub n satisfy |x sub n -0|< epsilon. From what you said |x sub n| = |x sub n -0| but I am not sure how this leads to lim(|x sub n|) = 0 from lim(x sub n)=0 or vice versa.

- Oct 11th 2008, 06:22 AMkalagota
well, by assumption, iff for every there exists a natural number such that for all we have ..

and from plato's post, the last in the equality is less than epsilon..

in the same manner, iff for every there exists a natural number such that for all we have ..