MATH 2360Q Lecture 4: Chapter 3.2

• School: UConn
• Department: Mathematics
• Course: MATH 2360Q
• Professor: Scott Zimmerman

Document Summary

Let p and q be any two points. (we want to say something about pq. To do so, we first need a line. ) If p q, set l to be the line containing them (which exists by the incidence postulate). If p=q, choose any other point r (which exists by the existence postulate), and set l to be the line containing them. Either way, l is a line containing p and q: by the ruler postulate, there are real numbers x and y corresponding to p and q with pq= |x-y| Since |x-y| 0, we have pq 0. Since the correspondence between l and the real numbers is one-to-one, this means p=q. Show: if p=q, then pq=0 (<=) assume p=q. A * c * b if and only if b * c * a. Even though we use the word between , we can"t assume it means what we think it should without proving it first.