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strict_partial_order [2013/09/04 17:26]
nikolaj
strict_partial_order [2014/03/21 11:11] (current)
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 ===== Strict partial order ===== ===== Strict partial order =====
-==== Definition ​==== +==== Set ==== 
-| @#88DDEE: $X$ |+| @#55CCEE: context ​    | @#55CCEE: $X$ |
  
-| @#FFBB00: $ <\ \in\ \text{StrictPartOrd}(X) $ |+| @#FFBB00: definiendum ​| @#FFBB00: $ <\ \in\ \text{StrictPartOrd}(X) $ |
  
-| @#88DDEE: $ <\ \in\ \mathrm{Rel}(X) $ |+| @#55CCEE: context ​    | @#55CCEE: $ <\ \in\ \mathrm{Rel}(X) $ |
 | $ x,y,z\in X $ | | $ x,y,z\in X $ |
  
-| @#55EE55: $ x \nless x $ | +| @#55EE55: postulate ​  | @#55EE55: $ x \nless x $ | 
-| @#55EE55: $ x<y\land y<z \implies x<z $ |+| @#55EE55: postulate ​  | @#55EE55: $ x<y\land y<z \implies x<z $ |
  
 Here we use infix notation: $x<y\ \equiv\ <(x,y)$. Here we use infix notation: $x<y\ \equiv\ <(x,y)$.
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 === Reference === === Reference ===
 Wikipedia: [[http://​en.wikipedia.org/​wiki/​Order_relation|Order theory]], [[http://​en.wikipedia.org/​wiki/​Poset|Poset]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Order_relation|Order theory]], [[http://​en.wikipedia.org/​wiki/​Poset|Poset]]
-==== Context ​====+==== Parents ​====
 === Subset of === === Subset of ===
 [[Reflexive relation]], [[Transitive relation]], [[Anti-symmetric relation]] [[Reflexive relation]], [[Transitive relation]], [[Anti-symmetric relation]]
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