The Limit of a Sequence
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چکیده
2. Claim. A sequence can have at most one limit. Proof: Suppose L and L′ be limits of a sequence. Then there exists an open interval I containing L and an open interval I ′ containing L′ and both of these intervals contain all but a finite number of terms of the sequence. If L 6= L′, I and I ′ can be chosen to be disjoint which (exercise) leads to a contradiction. Thus, it must be that L = L′.
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تاریخ انتشار 1998