Differences

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--- non-strict_partial_order [2013/09/04 17:43]
nikolaj
+++ non-strict_partial_order [2014/03/21 11:11] (current)
@@ Line 1: / Line 1: @@
 ===== Non-strict partial order =====
-==== Definition ====
+==== Set ====
-| @#88DDEE: $X$ |
+| @#55CCEE: context     | @#55CCEE: $X$ |
-| @#FFBB00: $ \le\ \in\ \mathrm{it} $ |
+| @#FFBB00: definiendum | @#FFBB00: $ \le\ \in\ \mathrm{it} $ |
 The relation $\le$ is an order relation if it's in the intersection of all reflexive, all anti-symmetric and all transitive relation. Hence
-| @#88DDEE: $ \le\ \in\ \mathrm{Rel}(X) $ |
+| @#55CCEE: context     | @#55CCEE: $ \le\ \in\ \mathrm{Rel}(X) $ |
 | $ x,y,z \in X $ |
-| @#55EE55: $ x \le x $ |
+| @#55EE55: postulate   | @#55EE55: $ x \le x $ |
-| @#55EE55: $ x\le y\ \land\ y\le x \implies (x=y) $ |
+| @#55EE55: postulate   | @#55EE55: $ x\le y\ \land\ y\le x \implies (x=y) $ |
-| @#55EE55: $ x \le y\ \land\ y \le z \Leftrightarrow x\le z $ |
+| @#55EE55: postulate   | @#55EE55: $ x \le y\ \land\ y \le z \Leftrightarrow x\le z $ |
 Here we use infix notation: $x\le y\ \equiv\ \le(x,y)$.
@@ Line 19: / Line 19: @@
 === Reference ===
 Wikipedia: [[http://en.wikipedia.org/wiki/Order_relation|Order theory]], [[http://en.wikipedia.org/wiki/Poset|Poset]]
-==== Context ====
+==== Parents ====
 === Subset of ===
 [[Reflexive relation]], [[Anti-symmetric relation]], [[Transitive relation]]
-=== Image of ===
+=== Equivalent to ===
 [[Poset]]