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** Existence of additive inverse: For any integer a, there exists an integer denoted by − a such that a + (− a )
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** and additive
** and inverse
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** and For
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** For example: One specific person may be identified by all of the following identifiers: Jane Smith ; Jane Elizabeth Meredith Smith ; Jane E. M. Smith ; Jane E. Smith ; Janie Smith ; Janie ; Little Janie ( as opposed to her mother or sister or cousin, Big Janie ); Aunt Jane ; Auntie Janie ; Mom ; Grandmom ; Nana ; Kelly's mother ; Billy's grandmother ; Ms. Smith ; Dr. Smith ; Jane E. Smith, PhD ; and Fuzzy ( her jocular nickname at work ).
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