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Let s

_{n}and t

_{n}be sequences. Suppose that lim s

_{n}= L (where s is a real number) and lim |s

_{n}- t

_{n}| = 0. Prove that lim t

_{n}= L.

I think this is going in the right way but i am not sure. If the lim a

_{n}= A, then lim |a

_{n}- A| = 0.

any help would be very nice.