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Question : 63

Total: 80

Let N be the set positive integers. For all n ∊ N, let fn=(n+1)1∕3−n1∕3 and
A={n∊N:f(n+1)<

<fn} Then

A = N
A is a finite set
the complement of A in N is nonempty but finite
A and its complement in N are both infinite

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