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Unformatted text preview: A has a least element. That is, there exists an element a A such that for all a A , a < a . Problem 3: (2 points) Consider the set of integers, Z . Prove that the multiplicative identity is unique. Proof: Suppose 1 and 1 are both multiplicative identities. Therefore, for all a Z (1) 1 a = a 1 = a, and (2) 1 a = a 1 = a. In particular (1) holds for a = 1 and (2) holds for a = 1 hence 1 = 1 1 = 1 1 = 1 . Therefore the multiplicative identity must be unique. 2...
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This note was uploaded on 10/18/2011 for the course MATH 19900 taught by Professor Schmidt during the Fall '07 term at UChicago.
- Fall '07