My Math Forum A poset exercise

 Applied Math Applied Math Forum

 June 8th, 2010, 08:42 PM #1 Senior Member   Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 A poset exercise I'm looking at a (rather old) lattice theory book, and in the first section there's this exercise: Let ? be a partial order on a set A. Show that there is a total order ?* such that a?b imples a?*b. (The author defines a partial order as a transitive, reflexive, anti-symmebtric relation, and a total order with the additional property that a?b or b?a.) The hint says to use Zorn's Lemma. While I can do this with liberal application of choice,this isn't particularly clean, and I'm judging by the hint (and the fact that choice has not been mentioned yet int he book) that there's a way to use Zorn's Lemma directly. I'd also guess this solution is much prettier. Any ideas on how to go about using Zorn's Lemma directly?

 Tags exercise, poset

### poset exercise

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post mahjk17 Applied Math 0 July 30th, 2012 06:44 PM mahjk17 Applied Math 0 July 28th, 2012 08:27 PM icemanfan Number Theory 2 March 15th, 2012 04:58 PM Touya Akira Abstract Algebra 8 May 10th, 2011 07:57 AM Noob1 Advanced Statistics 7 April 26th, 2010 05:55 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top