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i were thinking about this and it seen to me no, but a book i were reading says that the majorum of any set of integer is an element of that set. And if that's the case does it mean that the set of all integer have the least upper bound property.

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Set of integers have no supremum.But any finite set of integers have supremum which is maximum element of that set.

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Yes, it satisfies, in fact, in that case the sup is actually the maximum of the set.

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