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MyWikiBiz, Author Your Legacy — Friday May 03, 2024
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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>
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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>\texttt{(} a_1 \texttt{)} \texttt{(} a_2 \texttt{)} \texttt{(} a_3 \texttt{)}.\!</math>
    
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.
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