===== Non-strict partial order =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $X$ |

| @#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 

| @#55CCEE: context     | @#55CCEE: $ \le\ \in\ \mathrm{Rel}(X) $ |
| $ x,y,z \in X $ |

| @#55EE55: postulate   | @#55EE55: $ x \le x $ |
| @#55EE55: postulate   | @#55EE55: $ x\le y\ \land\ y\le x \implies (x=y) $ |
| @#55EE55: postulate   | @#55EE55: $ x \le y\ \land\ y \le z \Leftrightarrow x\le z $ |

Here we use infix notation: $x\le y\ \equiv\ \le(x,y)$.

==== Discussion ====
=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Order_relation|Order theory]], [[http://en.wikipedia.org/wiki/Poset|Poset]]
==== Parents ====
=== Subset of ===
[[Reflexive relation]], [[Anti-symmetric relation]], [[Transitive relation]]
=== Equivalent to ===
[[Poset]]