Consider F be the ordered field of rational functions and note that F has both N and R as subsets.
i) Illustrate that F doesn't have archimedean property. i.e., z>n for every n belongs to N.
ii) Illustrate that archimedean property (for each x>0 , there exists an n belongs to N such that 0< 1/n< x) doesn't apply. i.e., determine the positive member z in F such that, for all n belongs to N, 0
iii) Illustrate that F doesn't satisfy completeness axiom. i.e., fina a subset B of F such that B is bounded above, but B has no least upper bound. justify the answer.