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Let and are functions whose domains are subsets of , the set of positive integers. We say that is if there exist a positive real number and a positive integer such that for all
(b) Let us use the definition of 'f is (g)' to show that the following statements.
(I) Since for each positive integer we put and conclude that is
(ii) Let us show that is not Let us prove using the method by contradiction. Suppose that there exist a positive real number and a positive integer such that for all
It follows that for all Since we conclude that there exist such that for all This contradiction proves the statement.