My Math Forum  

Go Back   My Math Forum > College Math Forum > Applied Math

Applied Math Applied Math Forum

LinkBack Thread Tools Display Modes
January 21st, 2018, 09:02 AM   #1
Senior Member
Joined: Mar 2012
From: Belgium

Posts: 654
Thanks: 11

Extrapolating a partial ordering

Suppose we have a set $\displaystyle S$ and an order $\displaystyle \leq$ on most of the elements $\displaystyle s_1,s_2 \in S$. The problem is that the order is not defined for all pairs in $\displaystyle S$. Now how would I go and find an order $\displaystyle \preceq $ on S such that $\displaystyle s1 \preceq s2$ if $\displaystyle s1 \leq s2$ and such that all elements of $\displaystyle S$ are comparable for this order. What happens with contradictions in the original order ?

Last edited by gelatine1; January 21st, 2018 at 09:05 AM.
gelatine1 is offline  
January 21st, 2018, 09:53 AM   #2
Senior Member
Joined: Oct 2009

Posts: 733
Thanks: 246

Zorn's lemma.
Micrm@ss is offline  

  My Math Forum > College Math Forum > Applied Math

extrapolating, ordering, partial

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Extrapolating data Manishapattni Probability and Statistics 2 June 17th, 2016 11:27 AM
Well Ordering Theorem zylo Topology 23 January 14th, 2016 04:11 PM
Partial Ordering andmar Abstract Algebra 3 June 9th, 2011 05:26 AM
partial ordering, linearization poincare4223 Applied Math 1 March 25th, 2010 11:28 AM
Well-Ordering Proof jstarks4444 Number Theory 1 December 31st, 1969 04:00 PM

Copyright © 2019 My Math Forum. All rights reserved.