I wanted to check my understanding here.
Q1. Is is correct to say - Set of Natural Numbers (N) also has the Least Upper Bound Property. i.e. any non-empty subset of Natural Number, bounded above will have a least upper bound.
Q2. The above follows directly from the well-ordering principle of the Natural Numbers
Q3. Only difference I see between this property in Real Numbers and Natural Numbers is that in Natural Numbers the least upper bound will always be a element in the set, which might not be the case in Real Numbers
Thanks