Proposition: Every element in a vector space has a unique additive inverse. Proof: Suppose V is a vector space. Let v ∈ V. Suppose that w and w' are additive inverses of v. Then w' = w' + 0 = w' +(v + w) = (w'+v)+w = 0 + w = w. Thus w = w', as desired.
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eshi - (no access) - Sheldon_Axler_Linear_Algebra_Done_Right.pdf, p25
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