===== Strict partial order =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $X$ |

| @#FFBB00: definiendum | @#FFBB00: $ <\ \in\ \text{StrictPartOrd}(X) $ |

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

| @#55EE55: postulate   | @#55EE55: $ x \nless x $ |
| @#55EE55: postulate   | @#55EE55: $ x<y\land y<z \implies x<z $ |

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

==== Discussion ====
A strict partial order is automatically anti-symmetric.
=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Order_relation|Order theory]], [[http://en.wikipedia.org/wiki/Poset|Poset]]
==== Parents ====
=== Subset of ===
[[Reflexive relation]], [[Transitive relation]], [[Anti-symmetric relation]]