Unformatted text preview: a . Indeed,a =a + 0 by A3 =a + ( a + b ) by (*) = (a + a ) + b by A2 = 0 + b by A4 = b by A3 . Â± Lemma 3: For any a âˆˆ F , we have (1) Â· a =a . Proof: We compute 0 = 0 Â· a by Lemma 1 = (1 + (1)) Â· a by A4 = 1 Â· a + (1) Â· a by AM1 = a + (1) Â· a by M3 . By Lemma 2, we know that (a ) is the unique element of F with the property that a + (a ) = 0. Since we have shown that a + (1) Â· a = 0, it must be the case that (a ) = (1) Â· a . Â± 1...
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 Fall '10
 StevenKlee
 Calculus, Lemma

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