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Date: 9-1-2022
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Date: 11-1-2022
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Date: 26-12-2021
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Given a sequence of real numbers , the infimum limit (also called the limit inferior or lower limit), written and pronounced 'lim-inf,' is the limit of
as . Note that by definition, is nondecreasing, and so either has a limit or tends to . For example, suppose , then for odd, , and for even, . Another example is , in which case is a constant sequence .
When , the sequence converges to the real number
Otherwise, the sequence does not converge.
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