MATH 2360Q Lecture 5: Chapter 3.2 Cont.
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Math 2360q lecture 5 - chapter 3. 2 cont. Let l be a line, let a, b, and c be three distinct points that all lie on l, and let f: l ir be a coordinate function for l. (<=) suppose f(a)< f(c) < f(b) By algebra, |f(a) - f(c)| + |f(b) - f(c)| = |f(b) - f(a)| By the definition of a coordinate function, ac+cb=ab, and so c is between a and b. If f(a) > f(c) > f(b), the same argument works (=>) suppose c is between a and b. By definition, ac + cb = ab, so |f(a) - f(c)| + |f(b) - f(a)| (by definition of f) 3. 2. 14, either f(c) - f(a) and f(c) - f(b) are both positive or both negative. If both are positive, then f(c) > f(a) and f(b) > f(c) (which is what we wanted to prove)
