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, Calculation for proof 2. In order to prove proposition 2, we must show that m ? (? i )?(??)(?1)(m(? i ) ?
, Since m ? (? i ) ? ?m ? (? j ) = 0, the former expression is positive when (m(? i ) ?
, i )) ??1 > (?m(? j ) ? ?m(? j )) ??1 . Given that ? ? 1 < 0
, Remember that ? i > ? j , ? i > ? j and ? i > ? i . Moreover, by definition, ? i ? ? j =
, Calculation for proof 3, order to prove proposition 3, we must show that m ? (? i )?(m(? i ) ?
, Since m ? (? i ) ? ?m ? (? j ) = 0, the former expression is negative when (m(? i ) ?
, Remember that ? i > ? j , ? i > ? j and ? i < ? i . Moreover, by definition, ? i ? ? j =
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