- #1
podboy6
- 12
- 0
Okay, so I have a homework problem I'm a little confused about,
The textbook is pretty useless and we didn't go into types of orders very much in class. So, am I to show that the dictionary order is reflexive, antisymmetric, and transitive on XxX, since XxX is already linearly ordered? I hadn't even heard of the dictionary order until I saw this problem, so I'm a little confused as to how to start it off.
Let (X,[tex] \leq ) [/tex] be a linearly ordered set. Define the dictionary order, [tex] \preceq [/tex] on XxX by (x,y) [tex] \preceq [/tex] (x', y') if x=x' or if x=x' and y[tex] \leq [/tex]y'. Prove that the dictionary order is a linear order relation on XxX.
The textbook is pretty useless and we didn't go into types of orders very much in class. So, am I to show that the dictionary order is reflexive, antisymmetric, and transitive on XxX, since XxX is already linearly ordered? I hadn't even heard of the dictionary order until I saw this problem, so I'm a little confused as to how to start it off.