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maximal_extension_in_a_set [2014/12/04 14:18]
nikolaj
maximal_extension_in_a_set [2014/12/04 14:21]
nikolaj
Line 1: Line 1:
 ===== 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 $\mathrm{max}(a,​A)$ is the largest set in $X$ which encompasses $a$.+Given $a\in A$, the maximal extension $\mathrm{max}(a,​A)$ is the largest set in $A$ which encompasses $a$.
  
 === Predicate === === Predicate ===
-| @#EEEE55: predicate ​  | @#EEEE55: $x$ maximal in $X \equiv \mathrm{max}(x,​A)=x$ |+| @#EEEE55: predicate ​  | @#EEEE55: $x$ maximal in $X \equiv \mathrm{max}(x,​X)=x$ |
  
 === Reference === === Reference ===
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