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...Calculus a problems with solutions lecture problem show that if and b are any numbers is not equal to then there one only number x such this given by wearerequired two things the existence uniqueness of solution it enough check satises equation axiom m commutativity associativity inverse byaxiom therefore so let y be wehaveshownthatify isasolution which means unique actually secondpart oftheproofisenoughtoshowthestatementoftheproblem why notice application requires usingjust ordered eld axioms prove ab have opposite signs several methods for proving statement we will give here them in proof assume r already proved method checking all possible cases according o can three or each case weshowthatthestatement holds implies byaxioms hence thefact contradiction use multiply inequality times getting ruling out issimilar follows adding side using since thisfollowsfrom similarly as previous andthus different too cannot happen because would hold our assumption both implied complete weassume does...