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maximal_extension_in_a_set [2014/12/04 13:59] nikolaj |
maximal_extension_in_a_set [2014/12/04 14:17] nikolaj |
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| | @#55CCEE: context | @#55CCEE: $X$ ... set | | | @#55CCEE: context | @#55CCEE: $X$ ... set | | ||
| | @#55CCEE: context | @#55CCEE: $a\in X$ | | | @#55CCEE: context | @#55CCEE: $a\in X$ | | ||
| - | | @#FFBB00: definiendum | @#FFBB00: $\mathrm{max}(a,A)$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\mathrm{max}(a,A)\equiv\bigcup\{b\mid (b\in X)\land a\subseteq b}$ | |
| - | | @#55EE55: postulate | @#55EE55: $\mathrm{max}(a,A)\in X$ | | + | |
| - | | @#55EE55: postulate | @#55EE55: $a\subseteq\mathrm{max}(a,A)$ | | + | |
| - | | @#FFFDDD: forall | @#FFFDDD: $b\in X$ | | + | |
| - | | @#55EE55: postulate | @#55EE55: $a\subseteq b\implies b\subseteq \mathrm{max}(a,A)$ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | >todo: write this down order theoretical (define it in terms of an ordering defined via $\subseteq$) | ||
| === Idea === | === Idea === | ||
| Given $a\in X$, the maximal extension $a'$ is the largest amongs $X$ which does contain $a$. | Given $a\in X$, the maximal extension $a'$ is the largest amongs $X$ which does contain $a$. | ||
