How can we prove that the additive inverse -u is unique of a vector space?
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Assume that the vector u has two additive inverses, call them v and v' Then by definition: u + v 0 u + v' 0 Those two quantities are equal, so: u + v u + v' Now add v to the left side of each: v + u + v v + u + v' But we can say v+u 0 so: 0 + v 0 + v' v v'
