8. Suppose that Xn ::::: 0 for n E N. Under the interpretation 1/0 = 00 and

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8. Suppose that Xn ::::: 0 for n E N. Under the interpretation 1/0 = 00 and 1/00 = 0, prove that 1. 1 1 1m sup - = -----n--->

oo Xn lim infn---> 00 Xn and lim inf ~ = ___ 1 __ _ n--->oo Xn lim sUPn--->oo Xn

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