C3093109 - 1 α we get 1 α α x = 1 α That is 1 x = 1 α...

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9. (Statement of the problem.) Proof. (a) Take any x V . By A4, x + 0 = x . Multiplying both side by β , we get β ( x + 0 ) = β x . By A5, β x + β 0 = β x . Adding - β x , we get - β x + β x + β 0 = - β x + β x . By A4 and A3, - β x + β x + β 0 = 0 + β 0 = β 0 and - β x + β x = 0 . So β 0 = 0 . (b) Assume α x = 0. Suppose α 6 = 0.
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Unformatted text preview: 1 α we get 1 α α x = 1 α . That is, 1 x = 1 α . By A8 and part (a) of the problem (with β = 1 α ), x = . / 1...
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