MyWikiBiz, Author Your Legacy — Thursday November 07, 2024
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, 18:26, 23 June 2008
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| \PMlinkescapephrase{language} | | \PMlinkescapephrase{language} |
| \PMlinkescapephrase{Language} | | \PMlinkescapephrase{Language} |
| + | \PMlinkescapephrase{number} |
| + | \PMlinkescapephrase{Number} |
| \PMlinkescapephrase{object} | | \PMlinkescapephrase{object} |
| \PMlinkescapephrase{Object} | | \PMlinkescapephrase{Object} |
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| A \textbf{basic proposition}, \textbf{coordinate proposition}, or \textbf{simple proposition} in the universe of discourse $[a_1, \ldots, a_n]$ is one of the propositions in the set $\{ a_1, \ldots, a_n \}.$ | | A \textbf{basic proposition}, \textbf{coordinate proposition}, or \textbf{simple proposition} in the universe of discourse $[a_1, \ldots, a_n]$ is one of the propositions in the set $\{ a_1, \ldots, a_n \}.$ |
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− | Among the $2^{2^n}$ propositions in $[a_1, \ldots, a_n]$ are several families of $2^n$ propositions each that take on special forms with respect to the basis $\{ a_1, \ldots, a_n \}.$ | + | Among the $2^{2^n}$ propositions in $[a_1, \ldots, a_n]$ are several families of $2^n$ propositions each that take on special forms with respect to the basis $\{ a_1, \ldots, a_n \}.$ Three of these families are especially prominent in the present context, the \textit{singular}, the \textit{linear}, and the \textit{positive} propositions. Each family is naturally parameterized by the coordinate $n$-tuples in $\mathbb{B}^n$ and falls into $n + 1$ ranks, with a binomial coefficient $\binom{n}{k}$ giving the number of propositions that have rank or weight $k.$ |
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| $\ldots$ | | $\ldots$ |