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===Special Classes of Propositions===
===Special Classes of Propositions===
It is important to remember that the coordinate propositions {''a''<sub>''i''</sub>}, besides being projection maps ''a''<sub>''i''</sub> : '''B'''<sup>''n''</sup> → '''B''', are propositions on an equal footing with all others, even though employed as a basis in a particular moment. This set of ''n'' propositions may sometimes be referred to as the ''basic'' or ''simple'' propositions that found the universe of discourse. As typical and collective notations, we may use the forms {''a''<sub>''i''</sub> : '''B'''<sup>''n''</sup> → '''B'''} = ('''B'''<sup>''n''</sup> <font face=symbol>'''¸>'''</font> '''B''') to indicate the adoption of a set of ''a''<sub>''i''</sub> as a basis for discourse.
It is important to remember that the coordinate propositions <math>\{a_i\},</math> besides being projection maps <math>a_i : \mathbb{B}^n \to \mathbb{B},</math> are propositions on an equal footing with all others, even though employed as a basis in a particular moment. This set of <mat>n\!</math> propositions may sometimes be referred to as the ''basic'' or ''simple'' propositions that found the universe of discourse. As typical and collective notations, we may use the forms <math>\{a_i : \mathbb{B}^n \to \mathbb{B}\} = (\mathbb{B}^n \xrightarrow{i} \mathbb{B})</math> to indicate the adoption of a set of <math>a_i\!</math> as a basis for discourse.
Among the <math>2^{2^n}</math> propositions or functions in ('''B'''<sup>''n''</sup> → '''B''') are several fundamental sets of 2<sup>''n''</sup> propositions each that take on special forms with respect to a given basis <font face="lucida calligraphy">A</font> = {''a''<sub>''i''</sub>}. Three of these forms are especially common, the ''linear'', the ''positive'', and the ''singular''
Among the <math>2^{2^n}</math> propositions or functions in ('''B'''<sup>''n''</sup> → '''B''') are several fundamental sets of 2<sup>''n''</sup> propositions each that take on special forms with respect to a given basis <font face="lucida calligraphy">A</font> = {''a''<sub>''i''</sub>}. Three of these forms are especially common, the ''linear'', the ''positive'', and the ''singular''
