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Unformatted text preview: A has a least upper bound and we let w := lub A. It can be shown that w > 0. PROVE that w 2 = c. You may assume the Lemma given below. Lemma . Let u , a ∈ R with u > and a > . (i) If u 2 > a then there is an integer n ≥ 1 such that u-1 n > and ± u-1 n ² 2 > a. (ii) If u 2 < a then there is an integer n ≥ 1 such that ± u + 1 n ² 2 > a. 7. PROVE the following. (i) If n is prime and a · b = 0 in Z n then either a = 0 or b = 0 (in Z n ). (ii) If n is not prime then there exists a , b ∈ Z n with a 6 = 0 and b 6 = 0 such that a · b = 0 in Z n . 2...
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- Spring '08
- Prime number, Rational number, Multiplicative inverse, lub, following multiplication table