December 31st, 2016, 06:23 PM  #41  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,345 Thanks: 224  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.  

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negative, positive, poth, proof 
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