1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about linear order relations

  1. Mar 19, 2006 #1
    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.
  2. jcsd
  3. Mar 19, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I've usually heard it called "lexicographic order". Anyways...

    No it's not! XxX is just a set!

    Your goal is to show [itex](X \times X, \preceq)[/itex] is a total order...
    which means you have to do this.

    Just plow forward and do it. There's no trick to it, no cleverness is required: you just brute force your way through the logic. You know you're supposed to prove this ordering to be reflexive, antisymmetric, and transitive. So, just start trying to prove it reflexive! What does it mean for this ordering to be reflexive?
    Last edited: Mar 19, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Question about linear order relations