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power_set [2015/10/08 20:35]
nikolaj
power_set [2015/10/08 20:35] (current)
nikolaj
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 ----- -----
-=== Discussion === 
 Here we define Here we define
  
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 $\forall X.\,​\exists! P.\,\forall Y.\,​\left(Y\in P\Leftrightarrow Y\subseteq X\right)$ $\forall X.\,​\exists! P.\,\forall Y.\,​\left(Y\in P\Leftrightarrow Y\subseteq X\right)$
  
-The latter ​is short for+=== Discussion === 
 +The above is short for
  
 $\forall X.\,​\exists! P.\,\forall Y.\,​\left(Y\in P\Leftrightarrow \forall Z.\,(Z\in Y\implies Z\in X)\right)$ $\forall X.\,​\exists! P.\,\forall Y.\,​\left(Y\in P\Leftrightarrow \forall Z.\,(Z\in Y\implies Z\in X)\right)$
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Improvements of the human condition