December 31st, 2016, 07:23 PM  #41  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Quote:
Go ahead and define it. In fact your example is not a bijection because $(1 , 4)$ and $(3 , 12)$ both map to the same rational $\frac{1}{4}$ yet they are clearly 2 different points in the Cartesian plane. The reason Trichotomy is lost is because you are dealing with multi dimensional objects. For example , the following object $(1 , 4)$ as a point in the Cartesian plane is multi dimensional , in this case of dimension 2.  

Tags 
negative, positive, poth, proof 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Why did this change from positive to negative  Opposite  Algebra  2  September 17th, 2014 10:27 PM 
How do you know if it is positive or negative infinity?  SSJBartSimp  Calculus  1  June 11th, 2012 11:56 AM 
Positive and negative results  Ockonal  Calculus  5  December 4th, 2011 08:04 PM 
why the product of two negative integers is positive  fantom.1040  Algebra  7  June 28th, 2011 06:22 PM 
Positive and negative angles  David_Lete  Algebra  3  April 9th, 2009 06:03 AM 