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Elements Of Modern Algebra
- Prove by induction that if r is a real number where r1, then 1+r+r2++rn=1-rn+11-rarrow_forwardProve that if and are real numbers such that , then there exist a rational number such that . (Hint: Use Exercise 25 to obtain such that . Then choose to be the least integer such that . With these choices of and , show that and then that .) If and are positive real numbers, prove that there exist a positive integer such that . This property is called Archimedean Property of the real numbers. (Hint: If for all , then is an upper bound for the set . Use the completeness property of to arrive at a contradiction.)arrow_forwardName, in order, the five parts of the formal proof of a theorem.arrow_forward
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