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maximal_extension_in_a_set [2014/12/04 14:17] nikolaj |
maximal_extension_in_a_set [2014/12/04 14:19] nikolaj |
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| ===== Maximal extension in a set ===== | ===== Maximal extension in a set ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#55CCEE: context | @#55CCEE: $X$ ... set | | + | | @#55CCEE: context | @#55CCEE: $A$ ... set | |
| - | | @#55CCEE: context | @#55CCEE: $a\in X$ | | + | | @#55CCEE: context | @#55CCEE: $a\in A$ | |
| - | | @#FFBB00: definiendum | @#FFBB00: $\mathrm{max}(a,A)\equiv\bigcup\{b\mid (b\in X)\land a\subseteq b}$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\mathrm{max}(a,A)\equiv\bigcup\{b\mid b\in A\land a\subseteq b\}$ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| === Idea === | === Idea === | ||
| - | Given $a\in X$, the maximal extension $a'$ is the largest amongs $X$ which does contain $a$. | + | Given $a\in A$, the maximal extension $\mathrm{max}(a,A)$ is the largest set in $A$ which encompasses $a$. |
| === Predicate === | === Predicate === | ||
