MyWikiBiz, Author Your Legacy — Friday May 03, 2024
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, 02:24, 1 June 2013
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| </ul> | | </ul> |
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− | In each case the rank <math>k\!</math> ranges from <math>0\!</math> to <math>n\!</math> and counts the number of positive appearances of the coordinate propositions <math>a_1, \ldots, a_n\!</math> in the resulting expression. For example, for <math>n = 3,\!</math> the linear proposition of rank <math>0\!</math> is <math>0,\!</math> the positive proposition of rank <math>0\!</math> is <math>1,\!</math> and the singular proposition of rank <math>0\!</math> is <math>(a_1)(a_2)(a_3).\!</math> | + | In each case the rank <math>k\!</math> ranges from <math>0\!</math> to <math>n\!</math> and counts the number of positive appearances of the coordinate propositions <math>a_1, \ldots, a_n\!</math> in the resulting expression. For example, for <math>n = 3,\!</math> the linear proposition of rank <math>0\!</math> is <math>0,\!</math> the positive proposition of rank <math>0\!</math> is <math>1,\!</math> and the singular proposition of rank <math>0\!</math> is <math>\texttt{(} a_1 \texttt{)} \texttt{(} a_2 \texttt{)} \texttt{(} a_3 \texttt{)}.\!</math> |
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| The basic propositions <math>a_i : \mathbb{B}^n \to \mathbb{B}\!</math> are both linear and positive. So these two kinds of propositions, the linear and the positive, may be viewed as two different ways of generalizing the class of basic propositions. | | The basic propositions <math>a_i : \mathbb{B}^n \to \mathbb{B}\!</math> are both linear and positive. So these two kinds of propositions, the linear and the positive, may be viewed as two different ways of generalizing the class of basic propositions. |