(1.1) Using the field axioms of R (given in SG^(1), pg. 5), provide the solutions to Example 02.1 (a), (b) and (c), SG pg. 6. In each of your proofs you must indicate which field axiom(s) you are using, e.g. (Axiom A2), (Axiom M5), etc. (1.2) Prove that for each ninN,n0. State and use the field axioms of R in your proof as done in (1.1). (1.3)

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(1.1) Using the field axioms of R (given in SG^(1), pg. 5), provide the solutions to Example 02.1 (a), (b) and (c), SG pg. 6. In each of your proofs you must indicate which field axiom(s) you are using, e.g. (Axiom A2), (Axiom M5), etc. (1.2) Prove that for each ninN,n>0. State and use the field axioms of R in your proof as done in (1.1). (1.3) Prove that for every xinREEninN such that n>x. (1.4) Let (O)/()!=AsubeR and suppose that beta is a lower bound for A. Prove that beta =infAiffAAR epsi lon>0EEainA such that a< beta + epsi lon. (1.5) Let D={(2^(n)-1)/(2^(n))inR:ninN} Determine whether D is bounded in R. If so, find supD and infD. You must prove all your answers. [10] (1.6) Let (O)/()!=SsubeR such that S is bounded below. For kinR let kS={ks:sinS} If k<0, prove that kS is bounded above and supkS=kinfS. [6] (1.7) Give the solution to Activity 02.1(c), SG, pg. 9. [5]

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