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I was trying to prove that for the vector spaces, there is a unique vector that satisfy "u + 0 = u" and I used contradiction technique. The last point that I reached is [tex]u + 0_1 = u + 0_2[/tex]. However, I don't know whether I can say [tex]0_1 = 0_2[/tex] after this statement or there are some other operations that I must do (like this statement needs a proof as well?).

Thank you.

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# How to end the proof

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