Orders are binary relations on a set X. Here are some following properties that are assigned to orders. Antisymmetry $$a \leq b \; \mathrm{and} \; b \leq a \Rightarrow a = b$$ Transitivity $$a \leq b \; \mathrm{and} \; b \leq c \Rightarrow a \leq c$$ Connexity Either $$a \leq b \; \mathrm{or} \; b \leq a$$ Reflexitivity $$a \leq a$$ Total Order, Simple Order, Linear Order, Connex Order, Full Order. Find best way to do definitions